Category Theory - Part 3 of 6
summary
Covers concrete claims and examples: functors preserve identities and composition and can go between different categories; monoids model as one‑object categories; posets as categories give monotone maps = functors; list functor is faithful but not full with explicit Haskell examples (List, AllEmpty, A × Int); Cat is the category of small categories with functors as morphisms; shows how to check full/faithful, gives translations between languages as functor examples, and pauses for a group exercise to expand specific definitions.
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chapters (13)
- 0:00Introduction to functors
- 2:44Defining functors
- 4:48Functor structure
- 8:36Examples in functional programming
- 15:04Understanding objects
- 18:10Monotone maps and categories
- 23:40Clarifying functor mappings
- 25:37Monoid homomorphism functor
- 28:42The category of categories
- 34:06Morphisms in Cat
- 36:55Full and faithful functors
- 42:40Sets inside Cat
- 49:13Functor examples in Haskell
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