In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: homC(X, X) = {idX} for all objects XhomC(X, Y) = ∅ for all objects X ≠ Y Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set | homC(X, Y) | is 1 when X = Y and 0 when X is not equal to Y. Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category.

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• In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: homC(X, X) = {idX} for all objects XhomC(X, Y) = ∅ for all objects X ≠ Y Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set | homC(X, Y) | is 1 when X = Y and 0 when X is not equal to Y. Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category. (en)
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• 808519 (xsd:integer)
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• 665222630 (xsd:integer)
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http://purl.org/linguistics/gold/hypernym
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• In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: homC(X, X) = {idX} for all objects XhomC(X, Y) = ∅ for all objects X ≠ Y Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set | homC(X, Y) | is 1 when X = Y and 0 when X is not equal to Y. Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category. (en)
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• Discrete category (en)
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