[Merged by Bors] - feat(category_theory): braided and symmetric categories #3550
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| restate_axiom braided_category.braiding_naturality' | ||
| attribute [simp] braided_category.braiding_naturality |
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mark these reassoc too? and make the reassoc-ed version simp too, probably
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Done!
I also removed simp from the hexagon identities. We certainly weren't relying on these, and I think it may be better to wait for further applications before deciding on the best simp normal form. Likely we should reverse both hexagon equations, on the principle that the braidings "weigh more" than associators for simp normal form, but I think it's okay to wait here until someone actually wants simp to apply facts like this.
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Just the very basics: * the definition of braided and symmetric categories * braided functors, and compositions thereof * the symmetric monoidal structure coming from products * upgrading `Type u` to a symmetric monoidal structure This is prompted by the desire to explore modelling sheaves of modules as the monoidal category of module objects for an internal commutative monoid in sheaves of `Ab`. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Just the very basics:
Type uto a symmetric monoidal structureThis is prompted by the desire to explore modelling sheaves of modules as the monoidal category of module objects for an internal commutative monoid in sheaves of
Ab.