Category Theory MOC
A lot of terminology in category theory is motivated by the Category-vector space analogy.
Objects
The central object of category theory is, of course, the Category. We can reason about objects and morphisms in a category using a Commutative diagram.
Classification
See types of category.
Additional structure
- Category + Tensor product = Monoidal category
- Category + Internal hom = Closed category
Other properties
Not exactly a category
Internal constructions
Morphisms of categories
- Functor, Natural transformation
- Adjoint functor
- Equivalence of categories, Isomorphism of categories
External constructions
Categorification
- Categorification (Vertical)
- Oidification (Horizontal)
Categorical foundations
Issues
Bibliography
- @awodeyCategoryTheory2010
- @milewskiCategoryTheoryProgrammers2019
- @maclaneCategoriesWorkingMathematician1978
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