Theorems · Definition · category theory

CategoryTheory.Lax.LaxTrans.vComp

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G H : CategoryTheory.LaxFunctor B C} →
          CategoryTheory.Lax.LaxTrans F G → CategoryTheory.Lax.LaxTrans G H → CategoryTheory.Lax.LaxTrans F H

Vertical composition of lax transformations.

Defined in: Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax
Cited by: 5 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Bicategory CategoryTheory.Bicategory

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homproof · cited by 32,603
CategoryTheory.Bicategorystatement and proof · cited by 1,587
CategoryTheory.LaxFunctorstatement and proof · cited by 201
CategoryTheory.Lax.LaxTransstatement and proof · cited by 17
CategoryTheory.Lax.LaxTrans.vCompAppproof · cited by 3
CategoryTheory.Lax.LaxTrans.vCompNaturalityproof · cited by 3
CategoryTheory.Lax.LaxTrans.vComp_naturality_compproof · cited by 0
CategoryTheory.Lax.LaxTrans.vComp_naturality_idproof · cited by 0
CategoryTheory.Lax.LaxTrans.vComp_naturality_naturalityproof · cited by 0

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Lax.StrongTrans.vCompproof · cited by 3
CategoryTheory.Lax.StrongTrans.vComp_appstatement · cited by 0
CategoryTheory.Lax.StrongTrans.vComp_naturality_homstatement · cited by 0
CategoryTheory.Lax.StrongTrans.vComp_naturality_invstatement · cited by 0
CategoryTheory.Lax.StrongTrans.categoryStruct_comp_appstatement · cited by 0
CategoryTheory.Lax.StrongTrans.categoryStruct_comp_naturalitystatement · cited by 0