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Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence

Coherence tactic for monoidal categories #

We provide a monoidal_coherence tactic, which proves that any two morphisms (with the same source and target) in a monoidal category which are built out of associators and unitors are equal.

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Close the goal of the form η = θ, where η and θ are 2-isomorphisms made up only of associators, unitors, and identities.

example {C : Type} [Category C] [MonoidalCategory C] :
  (λ_ (𝟙_ C)).hom = (ρ_ (𝟙_ C)).hom := by
  monoidal_coherence
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    Close the goal of the form η = θ, where η and θ are 2-isomorphisms made up only of associators, unitors, and identities.

    example {C : Type} [Category C] [MonoidalCategory C] :
      (λ_ (𝟙_ C)).hom = (ρ_ (𝟙_ C)).hom := by
      monoidal_coherence
    
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    Instances For