📚 node [[20210116154952 category]]

A category is specified by four characteristics:

  1. Objects, $X$

  2. 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 $Hom(X,Y)$)

  3. Identitiy morphisms, a morphism $X \to X$

  4. Composition. Given morphisms f and g, there exists a morphism h such that $h = f \circ g$

Additionally, categories adhere to the following conditions:

  1. Unitality: for any morphism in the category $X \to Y$, $id_x \circ f f f \circ id_y#$

  2. Associativity: given morphisms f, g, and h in the category, $(f \circ g) \circ h = f \circ (g \circ h)$

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