Theorems · Inductive type · category theory

CategoryTheory.Oplax.LaxTrans.Modification

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G : CategoryTheory.OplaxFunctor B C} → (F ⟶ G) → (F ⟶ G) → Type (max u₁ w₂)

A modification Γ between lax natural transformations η and θ (between oplax functors) consists of a family of 2-morphisms Γ.app a : η.app a ⟶ θ.app a, which satisfies the equation (app a ▷ G.map f) ≫ θ.naturality f = η.naturality f ≫ (F.map f ◁ app b) for each 1-morphism f : a ⟶ b.

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

18 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory