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title: "category"
source: https://www.jemoka.com/posts/kbhcategory/
---

A category is an abstract collection of objects
constituents collection of objects, where if \(X\) is an object of \(C\) we write \(X \in C\) for a pair of objects \(X, Y \in C\), a set of morphisms acting upon the objects which we call the homset additional information requirements there exists the identity morphism; that is, \(\forall X \in C, \exists I_{X}: X\to X\) morphisms are always composable: given \(f: X\to Y\), and \(g: Y\to Z\), exists \(gf: X \to Z\) the identity morphism can compose in either direction: given \(f: X \to Y\), then \(f I_{x} = f = I_{y} f\) morphism composition is associative: \((hg)f=h(gf)\)
