Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Lax.LaxTrans.Modification.app

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G : CategoryTheory.LaxFunctor B C} →
          {η θ : F ⟶ G} → CategoryTheory.Lax.LaxTrans.Modification η θ → (a : B) → η.app a ⟶ θ.app a

The underlying family of 2-morphisms.

Defined in
Mathlib.CategoryTheory.Bicategory.Modification.Lax
Cited by
28 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.BicategoryCategoryTheory.Bicategory

Around this declaration

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

CategoryTheory.Lax.LaxTrans.Modification.ext · cited by 2Modification.extCategoryTheory.Lax.LaxTrans.homCategory.ext · cited by 1homCategory.extCategoryTheory.Lax.LaxTrans.whiskerLeft · cited by 1LaxTrans.whiskerLeftCategoryTheory.Lax.LaxTrans.whiskerRight · cited by 1LaxTrans.whiskerRightCategoryTheory.Lax.LaxTrans.Modification.naturality · cited by 1Modification.naturalityCategoryTheory.Lax.LaxTrans.Modification.vcomp · cited by 1Modification.vcompCategoryTheory.Lax.LaxTrans.associator_inv_as_app · cited by 0LaxTrans.associator_inv_a…CategoryTheory.Lax.LaxTrans.homCategory_comp_as_app · cited by 0LaxTrans.homCategory_comp…CategoryTheory.Lax.LaxTrans.homCategory_id_as_app · cited by 0LaxTrans.homCategory_id_a…CategoryTheory.Lax.LaxTrans.homCategory.ext_iff · cited by 0homCategory.ext_iffCategoryTheory.Lax.LaxTrans.isoMk_hom_as_app · cited by 0LaxTrans.isoMk_hom_as_appCategoryTheory.Lax.LaxTrans.isoMk_inv_as_app · cited by 0LaxTrans.isoMk_inv_as_appCategoryTheory.Lax.LaxTrans.leftUnitor_hom_as_app · cited by 0LaxTrans.leftUnitor_hom_a…CategoryTheory.Lax.LaxTrans.leftUnitor_inv_as_app · cited by 0LaxTrans.leftUnitor_inv_a…CategoryTheory.Lax.LaxTrans.rightUnitor_hom_as_app · cited by 0LaxTrans.rightUnitor_hom_…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryPrefunctor.obj · cited by 1241Prefunctor.objCategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct · cited by 1154PrelaxFunctor.toPrelaxFun…CategoryTheory.PrelaxFunctorStruct.toPrefunctor · cited by 1142PrelaxFunctorStruct.toPre…CategoryTheory.LaxFunctor.toPrelaxFunctor · cited by 216LaxFunctor.toPrelaxFunctorCategoryTheory.LaxFunctor · cited by 201CategoryTheory.LaxFunctorCategoryTheory.Lax.LaxTrans.app · cited by 61LaxTrans.appCategoryTheory.Lax.LaxTrans.Modification · cited by 14LaxTrans.ModificationModification.appCITED BYCITES

Cites9

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

Cited by31

Results whose statement or proof uses this declaration.