[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"OGjvkD5HBM":3},"# KittyCats\n\nA Lean formalization of undergraduate category theory built from first principles with no Mathlib.\n\n- [Category](KittyCats/Category.lean) - categories, composition, identity, and the opposite category\n- [Functor](KittyCats/Functor.lean) - functors, identity functor, functor composition\n- [NatTrans](KittyCats/NatTrans.lean) - natural transformations, vertical composition, natural isomorphisms\n- [Morphism](KittyCats/Morphism.lean) - isomorphisms, monomorphisms, epimorphisms, split monos/epis, groupoids\n- [Product](KittyCats/Product.lean) - the product of two categories\n- [Limits](KittyCats/Limits.lean) - terminal and initial objects, categorical products, coproducts\n- [Cartesian](KittyCats/Cartesian.lean) - cartesian and cocartesian categories, diagonal, product maps\n- [Monoidal](KittyCats/Monoidal.lean) - monoidal, braided, and symmetric monoidal categories\n- [Closed](KittyCats/Closed.lean) - exponential objects, cartesian closed categories\n- [Dual](KittyCats/Dual.lean) - the duality principle: terminal/initial, product/coproduct, mono/epi via Op\n- [Equiv](KittyCats/Equiv.lean) - equivalence of categories, the Op involution\n- [Instances](KittyCats/Instances.lean) - the category of types as a cartesian closed category\n- [Adjunction](KittyCats/Adjunction.lean) - adjunctions via unit/counit with triangle identities\n- [Monad](KittyCats/Monad.lean) - monads, Kleisli categories, monads as monoids in the category of endofunctors\n- [Thm](KittyCats/Thm.lean) - naturality of pairing, diagonal absorption, and the curry/eval adjunction\n- [Yoneda](KittyCats/Yoneda.lean) - presheaves, the Yoneda lemma, fully faithful embedding\n\n## Refs\n\n- Steve Awodey, _Category Theory_ (2nd edition, Oxford Logic Guides, 2010).\n- Saunders Mac Lane, _Categories for the Working Mathematician_ (2nd edition, Springer GTM, 1998).\n\n## License\n\nMIT\n",1780846761681]