mathlib3
965f46d4 - feat(category_theory/monoidal): coherence tactic (#13125)

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4 years ago
feat(category_theory/monoidal): coherence tactic (#13125) This is an alternative to #12697 (although this one does not handle bicategories!) From the docstring: ``` Use the coherence theorem for monoidal categories to solve equations in a monoidal equation, where the two sides only differ by replacing strings of "structural" morphisms with different strings with the same source and target. That is, `coherence` can handle goals of the form `a ≫ f ≫ b ≫ g ≫ c = a' ≫ f ≫ b' ≫ g ≫ c'` where `a = a'`, `b = b'`, and `c = c'` can be proved using `coherence1`. ``` This PR additionally provides a "composition up to unitors+associators" operation, so you can write ``` example {U V W X Y : C} (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) : U ⟶ Y := f ⊗≫ g ``` Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: yuma-mizuno <mizuno.y.aj@gmail.com>
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