Theorems · Definition · category theory

CategoryTheory.Lax.StrongTrans.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.StrongTrans F G → CategoryTheory.Lax.StrongTrans G H → CategoryTheory.Lax.StrongTrans F H

Vertical composition of strong natural transformations.

Defined in: Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax
Cited by: 3 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Bicategory CategoryTheory.Bicategory

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Cites19

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.PrelaxFunctor.toPrelaxFunctorStructproof · cited by 1,154
CategoryTheory.PrelaxFunctorStruct.toPrefunctorproof · cited by 1,142
CategoryTheory.Iso.symmproof · cited by 993
Prefunctor.mapproof · cited by 952
CategoryTheory.Iso.transproof · cited by 566
CategoryTheory.Bicategory.associatorproof · cited by 405
CategoryTheory.LaxFunctor.toPrelaxFunctorproof · cited by 216
CategoryTheory.LaxFunctorstatement and proof · cited by 201
CategoryTheory.Lax.LaxTrans.appproof · cited by 61
CategoryTheory.Bicategory.whiskerRightIsoproof · cited by 50

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Lax.StrongTrans.categoryStructproof · cited by 4
CategoryTheory.Lax.StrongTrans.vComp_appstatement and proof · cited by 0
CategoryTheory.Lax.StrongTrans.vComp_naturality_homstatement and proof · cited by 0
CategoryTheory.Lax.StrongTrans.vComp_naturality_invstatement · cited by 0