MathGloss

A category $\mathcal C$ is a collection of objects together with a set $\mathcal C(A,B)$ of morphisms or maps between any two objects. In particular, there is always for each object $A$ in $\mathcal C$ an identity morphism $\text{id}_A \in\mathcal C(A,A)$. Finally, a category must obey the following composition law: $$\circ: \mathcal C(B,C)\times \mathcal C(A,B) \to \mathcal C(A,C)$$ for all triples $A$, $B$, $C$ of objects such that composition is associative, and identity morphisms are identities for composition. That is,

• $h\circ(g\circ f) = (h\circ g)\circ f$;
• $\text{id}\circ f = f$;
• $f\circ \text{id} = f$.

Wikidata ID: Q719395

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