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Category Theory β€” Discuss categories, functors, natural transformations, adjunctions, monads, toposes, ∞-categories, and their deep connections to type theory and functional programming. nya~
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πŸ“ Subforums: Homotopy Type Theory Applied Category Theory Topos Theory ∞-Categories Enriched Categories 🐾 Category Memes & Shitposts
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πŸ“Œ [READ FIRST] Rules & Resources for the Category Theory subforum β€” textbooks, nLab links, Haskell bridges
STICKY by MewMorphism  Β·  Jan 03, 2024
12 4,821 by CubicalCat Feb 14, 2026  11:47 PM
πŸ“Œ [STICKY] CGPA Glossary: Category Theory Edition β€” Objects, Morphisms, Functors, nya~ explained for new cat girls
STICKY by ToposTail  Β·  Dec 22, 2023
29 7,093 by KleisliKitten Mar 15, 2026  02:33 AM
πŸ”₯ "A monad is just a monoid in the category of endofunctors" β€” what does this ACTUALLY mean? is the t-shirt correct??
HOT by MewMorphism  Β·  Mar 01, 2026
147 9,334 by FunctorFelyne Mar 27, 2026  03:59 AM
πŸ’¬ The Yoneda Lemma: can someone give an intuitive explanation without lying too much? 😿
NEW by CubicalCat  Β·  Mar 24, 2026
38 1,204 by ToposTail Mar 27, 2026  01:14 AM
πŸ’¬ Adjunctions are EVERYWHERE and it's making me cry (a list: free/forgetful, curry/uncurry, Ξ£/Ξ  types, ...)
by ToposTail  Β·  Mar 20, 2026
54 2,871 by MewMorphism Mar 26, 2026  10:52 PM
πŸ’¬ Natural transformations as "morphisms of functors" β€” vertical vs horizontal composition, whiskering, the interchange law
by KleisliKitten  Β·  Mar 18, 2026
22 983 by CubicalCat Mar 25, 2026  07:41 PM
πŸ“– Is Hask actually a category? The fast-and-loose reasoning thread (bottoms, seq, unsafePerformIO...)
ONGOING by FunctorFelyne  Β·  Mar 12, 2026
91 4,450 by PurrfectPullback Mar 24, 2026  09:05 PM
πŸ’¬ Toposes and the subobject classifier Ξ© β€” why does this generalize Set so elegantly? (w/ a cat girl diagram attempt)
by ToposTail  Β·  Mar 10, 2026
33 1,566 by SheafSiamese Mar 23, 2026  04:18 AM
πŸ’¬ Kleisli categories and computational effects β€” Moggi's insight explained from scratch, no prior CT needed
NEW by MewMorphism  Β·  Mar 22, 2026
15 612 by MewMorphism Mar 26, 2026  11:00 PM
πŸ”₯ ∞-Categories: quasicategories vs Segal spaces vs complete Segal spaces β€” why are there so many models and which one should I use??
HOT by CubicalCat  Β·  Feb 28, 2026
112 5,880 by ToposTail Mar 27, 2026  02:37 AM
πŸ’¬ Limits, colimits, and universal properties β€” product types are products! sum types are coproducts! pullbacks??
by PurrfectPullback  Β·  Mar 05, 2026
44 2,103 by KleisliKitten Mar 21, 2026  06:55 PM
πŸ’¬ The Curry–Howard–Lambek correspondence: propositions=types=objects, proofs=programs=morphisms. Mind officially blown.
DISCUSSION by CubicalCat  Β·  Mar 08, 2026
67 3,299 by MewMorphism Mar 22, 2026  08:12 PM
πŸ’¬ Kan Extensions: "all concepts are Kan extensions" β€” coend calculus, comma categories, and why this matters for type theory
by SheafSiamese  Β·  Feb 20, 2026
19 877 by ToposTail Mar 20, 2026  12:40 AM
βœ… [SOLVED] Monoidal categories and tensor products β€” I finally understand braided monoidal cats and I made ASCII art to celebrate
SOLVED by FunctorFelyne  Β·  Feb 15, 2026
26 1,450 by CubicalCat Mar 18, 2026  05:03 PM
πŸ’¬ Eilenberg–Moore algebras vs Kleisli category: two ways to decompose a monad, which one is more fun? (poll inside)
by KleisliKitten  Β·  Feb 10, 2026
35 1,712 by PurrfectPullback Mar 16, 2026  10:22 PM
πŸ’¬ Enriched category theory for dummies (me) β€” hom-sets β†’ hom-objects, V-categories, Ab-enriched = preadditive categories
by MewMorphism  Β·  Feb 03, 2026
17 690 by SheafSiamese Mar 14, 2026  03:15 AM
πŸ”₯ Grothendieck toposes, sheaves, and why a topos is like a "generalized space" β€” guest post by SheafSiamese 🐈
HOT MROWL✨ by SheafSiamese  Β·  Jan 29, 2026
88 4,007 by ToposTail Mar 25, 2026  11:58 PM
πŸ’¬ Free–forgetful adjunctions: free monoids, free groups, free vector spaces β€” the universal property machine go brr
by PurrfectPullback  Β·  Jan 22, 2026
41 1,934 by FunctorFelyne Mar 19, 2026  08:33 PM
πŸ’¬ Cubical Type Theory and its categorical semantics β€” cubical sets, connections, compositions in CubicalCat's favourite topic
NEW by CubicalCat  Β·  Mar 25, 2026
8 344 by CubicalCat Mar 27, 2026  12:55 AM
πŸ’¬ Duality principle: opposite categories, contravariant functors, and why every theorem gives you a free theorem
by KleisliKitten  Β·  Jan 14, 2026
21 908 by MewMorphism Mar 11, 2026  04:44 AM
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