Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Oplax.OplaxTrans.vcomp

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G H : CategoryTheory.OplaxFunctor B C} →
          CategoryTheory.Oplax.OplaxTrans F G →
            CategoryTheory.Oplax.OplaxTrans G H → CategoryTheory.Oplax.OplaxTrans F H

Vertical composition of oplax transformations.

Defined in
Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
Cited by
7 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.BicategoryCategoryTheory.Bicategory
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Oplax.OplaxTrans.categoryStruct · cited by 49OplaxTrans.categoryStructCategoryTheory.Oplax.StrongTrans.vcomp · cited by 5StrongTrans.vcompCategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_inv · cited by 0StrongTrans.categoryStruc…CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_app · cited by 0StrongTrans.categoryStruc…CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality · cited by 0StrongTrans.categoryStruc…CategoryTheory.Pseudofunctor.StrongTrans.categoryStruct_comp_naturality_hom · cited by 0StrongTrans.categoryStruc…CategoryTheory.Oplax.StrongTrans.vcomp_app · cited by 0StrongTrans.vcomp_appCategoryTheory.Oplax.StrongTrans.vcomp_naturality_hom · cited by 0StrongTrans.vcomp_natural…CategoryTheory.Oplax.StrongTrans.vcomp_naturality_inv · cited by 0StrongTrans.vcomp_natural…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct · cited by 1154PrelaxFunctor.toPrelaxFun…CategoryTheory.PrelaxFunctorStruct.toPrefunctor · cited by 1142PrelaxFunctorStruct.toPre…Prefunctor.map · cited by 952Prefunctor.mapCategoryTheory.Bicategory.whiskerRight · cited by 531Bicategory.whiskerRightCategoryTheory.Bicategory.whiskerLeft · cited by 524Bicategory.whiskerLeftCategoryTheory.Bicategory.associator · cited by 405Bicategory.associatorCategoryTheory.OplaxFunctor · cited by 253CategoryTheory.OplaxFunct…CategoryTheory.OplaxFunctor.toPrelaxFunctor · cited by 246OplaxFunctor.toPrelaxFunc…CategoryTheory.Oplax.OplaxTrans.app · cited by 76OplaxTrans.appCategoryTheory.Oplax.OplaxTrans.naturality · cited by 38OplaxTrans.naturalityOplaxTrans.vcompCITED BYCITES

Cites16

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

Cited by9

Results whose statement or proof uses this declaration.