[Merged by Bors] - feat: port Algebra.Category.Mon.Basic #2902
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Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
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Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
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I think the ports * #2902 (MonCat) * #3036 (GroupCat) * #3260 (ModuleCat) didn't quite get things right, and also have some variation between them. This PR tries to straighten things out. Major changes: * Have the coercion to type be via `X.\a`, and put attribute `@[coe]` on this. * Make sure the coercion from morphisms to functions means that simp lemmas about the underlying bundled morphisms apply directly. * This means we drop lemmas like ``` lemma Hom.map_mul {X Y : MonCat} (f : X ⟶ Y) (x y : X) : ((forget MonCat).map f) (x * y) = f x * f y ``` * But at the expense of adding lemmas like ``` lemma coe_comp {X Y Z : MonCat} {f : X ⟶ Y} {g : Y ⟶ Z} : (f ≫ g : X → Z) = g ∘ f := rfl ``` Overall I'm pretty happy, and it allows me to unstick the long stuck #3105. This is not everything I want to do to refactor these files, but once I was satisfied that I can move forward with RingCat, I want to get this merged so we can unblock porting progress. I'll promise to come back to this soon! :-) Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>
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The file/directory/category
Monwas renamed asMonCat. A few new definitions and simp lemmas were necessary in order to make this port and ease automation, see the porting notes.