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The Hom-set Definition of Mathematical Categories |
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The original definition of a category is in terms of a set S of objects and a set A of arrows linking the elements of S. The hom-set of objects x and y in category C is the set of all arrows in C with a domain of x and a codomain of y. It is denoted as
Alternatively a category could be defined as:
This composition function may be expressed as <f, g> → f°g for f ∈ hom(y, z) and g ∈ hom(x, y).
(To be continued.)
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