Basic monoidal category theory #364
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Markdown apparently specifies that the numbers are ignored in ordered lists, so we can't use them for "sparse" enumerations.
Add some combinators for reasoning with ternary compositions, expose F-map-iso in Cat.Functor.Reasoning, expose more reasoning modules for monoidal categories.
- reverse monoidal categories - braided, symmetric monoidal categories - monoidal categories with diagonals - cartesian monoidal categories are symmetric monoidal with diagonals - (lax) monoidal functors, braided/symmetric/diagonal monoidal functors, monoidal natural transformations - monoidal functors take monoids to monoids, functorially - a bunch of extra coherence properties for monoidal and braided monoidal categories - tensorial strengths, equivalence between left and right strengths in a braided monoidal category, every Sets-endofunctor is strong
plt-amy
approved these changes
Feb 29, 2024
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Description
My initial motivation was to understand the precise relationship between (symmetric) monoidal monads and commutative strong monads, which is why I'm formalising strengths here, but that page could use more prose. Edits welcome.
Some proofs are truly nightmarish, and I feel like we're still missing some important reasoning combinators for isomorphisms but I don't want to think about it right now.
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