|San José State University|
& Tornado Alley
in Category Theory
A category is a collection of objects and a collection of arrows between those object. The collection of arrows is closed under composition. A functor is mapping between two categories. Because any cateory involves two collections, objects and arrows, a functor has to involve two mappings; one mapping between the object collections of the two categories and another between the arrow collections.
The functor mappings have satisfy further conditions. Let the two categories for a functor be denoted as C and D and a functor between them as F:C → D. Just for this presentation think of C and D as the order pairs (CO, CA) and (DO, DA). Likewise F is an ordered pair (FO, FA) where
The conditions which F must satisfy are:
The remarable and beautiful thing is that the collection of categories with functors as the collection of arrows is a CATEGORY!
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