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    "0007": {
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    "0008": {
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        "declaration": []
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    "0010": {
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    "0011": {
        "domain": [
            "Category"
        ],
        "level": "High",
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            "Basic"
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        "reference": "Exercise 9D, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0012": {
        "domain": [
            "Category"
        ],
        "level": "High",
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            "Basic"
        ],
        "reference": "Exercise 7P, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0013": {
        "domain": [
            "Category"
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        "level": "High",
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        "reference": "3.39 EXAMPLES (6), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
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    },
    "0014": {
        "domain": [
            "Category"
        ],
        "level": "High",
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        ],
        "reference": "9.3 EXAMPLES (2), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0015": {
        "domain": [
            "Category"
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        "level": "High",
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        "reference": "9.3 EXAMPLES (2)(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
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    },
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        "domain": [
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        "reference": "9.3 EXAMPLES (3)(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
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    },
    "0017": {
        "domain": [
            "Category"
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        "level": "High",
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        "reference": "9.3 EXAMPLES (4)(d), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
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    },
    "0018": {
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            "Category"
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        "level": "High",
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        "reference": "9.3 EXAMPLES (4)(a), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0019": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0020": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0021": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0022": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0023": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0024": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0025": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0026": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "Exercise 19I, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0027": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "Exercise 18H, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0028": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Adjunction"
        ],
        "reference": "Exercise 19F (a), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0029": {
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            "Category"
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        "tag": [
            "Adjunction"
        ],
        "reference": "",
        "declaration": []
    },
    "0030": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Reflective"
        ],
        "reference": "Exercise 4G(d), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
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    },
    "0031": {
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            "Category"
        ],
        "level": "High",
        "tag": [
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        ],
        "reference": "Exercise 4E(d), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0032": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Reflective"
        ],
        "reference": "Exercise 4D(a), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0033": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Reflective"
        ],
        "reference": "Exercise 4D(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0034": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 10R, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0035": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 5O(k), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0036": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 5J(d), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0037": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 5D(d), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0038": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 10L, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0039": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 5L, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0040": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 8G(a), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0041": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Concrete"
        ],
        "reference": "Exercise 8G(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0042": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0043": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0044": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0045": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0046": {
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            "Category"
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        "level": "Easy",
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    "0047": {
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    "0048": {
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        "tag": [
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        "declaration": []
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    "0049": {
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            "Category"
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        "tag": [
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    "0050": {
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        "level": "Medium",
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            "Limit"
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        "declaration": []
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    "0051": {
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            "Category"
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        "level": "Medium",
        "tag": [
            "Limit"
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        "reference": "",
        "declaration": []
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    "0052": {
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            "Category"
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        "reference": "",
        "declaration": []
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    "0053": {
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            "Limit"
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        "declaration": []
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    "0054": {
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        "level": "Medium",
        "tag": [
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        ],
        "reference": "",
        "declaration": []
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    "0055": {
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            "Category"
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        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0056": {
        "domain": [
            "Category"
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        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0057": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 13F, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0058": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0059": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 13D(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0060": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0061": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0062": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 12N(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0063": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0064": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0065": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0066": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 12N(c), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0067": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0068": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0069": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 11O, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0070": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 13C, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0071": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 13D(a), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0072": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Limit"
        ],
        "reference": "Exercise 12K, Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0073": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Limit"
        ],
        "reference": "",
        "declaration": []
    },
    "0074": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Cocompletion"
        ],
        "reference": "Corollary A.5, Jiří Adámek, Liang-Ting Chen, Stefan Milius, and Henning Urbat, Reiterman's Theorem on Finite Algebras for a Monad, arXiv:2101.00942",
        "declaration": []
    },
    "0075": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Cocompletion"
        ],
        "reference": "Proposition 3.2, Chen Ruiyuan 2021, On sifted colimits in the presence of pullbacks, arXiv:2109.12708",
        "declaration": []
    },
    "0076": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Cocompletion"
        ],
        "reference": "Jiří Adámek, Liang-Ting Chen, Stefan Milius, and Henning Urbat, Reiterman's Theorem on Finite Algebras for a Monad, arXiv:2101.00942",
        "declaration": []
    },
    "0077": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Cocompletion"
        ],
        "reference": "Theorem 5.1, Chen Ruiyuan 2021, On sifted colimits in the presence of pullbacks, arXiv:2109.12708",
        "declaration": []
    },
    "0078": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Cocompletion"
        ],
        "reference": "Lemma 6.2, Chen Ruiyuan 2021, On sifted colimits in the presence of pullbacks, arXiv:2109.12708",
        "declaration": []
    },
    "0079": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0080": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0081": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0082": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0083": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0084": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0085": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0086": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0089": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0087": {
        "domain": [
            "Category"
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        "level": "High",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0088": {
        "domain": [
            "Category"
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        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0090": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Abelian"
        ],
        "reference": "",
        "declaration": []
    },
    "0091": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0092": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0093": {
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            "Category"
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        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0094": {
        "domain": [
            "Category"
        ],
        "level": "Easy",
        "tag": [
            "Monad"
        ],
        "reference": "Exercise 20F(b), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0095": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0096": {
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        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0097": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0098": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    },
    "0099": {
        "domain": [
            "Category"
        ],
        "level": "Medium",
        "tag": [
            "Monad"
        ],
        "reference": "Exercise 20F(c), Adámek, J., Herrlich, H. and Strecker, G., 1990. Abstract and concrete categories. Wiley-Interscience.",
        "declaration": []
    },
    "0100": {
        "domain": [
            "Category"
        ],
        "level": "High",
        "tag": [
            "Monad"
        ],
        "reference": "",
        "declaration": []
    }
}