📕 subnode [[@ryan/20210116154952 category]]
in 📚 node [[20210116154952category]]

tags :: category theory

source :: ACT4E  Session 1  Transmutation
A category is specified by four characteristics:

Objects, $X$

Morphisms, $X \to Y$. For every pair of objects in a category there exists a set whose elements map X to Y (this set could be called $Hom(X,Y)$)

Identitiy morphisms, a morphism $X \to X$

Composition. Given morphisms f and g, there exists a morphism h such that $h = f \circ g$
Additionally, categories adhere to the following conditions:

Unitality: for any morphism in the category $X \to Y$, $id_x \circ f
f
f \circ id_y#$ 
Associativity: given morphisms f, g, and h in the category, $(f \circ g) \circ h = f \circ (g \circ h)$
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