mathlib
52c0b421 - feat(category_theory): Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D (#3576)

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5 years ago
feat(category_theory): Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D (#3576) When `D` is a monoidal category, monoid objects in `C ⥤ D` are the same thing as functors from `C` into the monoid objects of `D`. This is formalised as: * `Mon_functor_category_equivalence : Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D` The intended application is that as `Ring ≌ Mon_ Ab` (not yet constructed!), we have `presheaf Ring X ≌ presheaf (Mon_ Ab) X ≌ Mon_ (presheaf Ab X)`, and we can model a module over a presheaf of rings as a module object in `presheaf Ab X`. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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