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Theorems · Definition · category theory

CategoryTheory.Bicategory.postcomposingCat

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    (a b c : B) → CategoryTheory.Functor (b ⟶ c) (CategoryTheory.Cat.of (a ⟶ b) ⟶ CategoryTheory.Cat.of (a ⟶ c))

Version of Bicategory.postcomposing viewed in the bicategory Cat.

Defined in
Mathlib.CategoryTheory.Bicategory.Yoneda
Cited by
18 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Bicategory

Around this declaration

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

CategoryTheory.Bicategory.postcomposing₂ · cited by 10Bicategory.postcomposing₂CategoryTheory.Bicategory.postcomp₂ · cited by 6Bicategory.postcomp₂CategoryTheory.Bicategory.associatorNatIsoLeftCat · cited by 2Bicategory.associatorNatI…CategoryTheory.Bicategory.associatorNatIsoMiddleCat · cited by 2Bicategory.associatorNatI…CategoryTheory.Bicategory.rightUnitorNatIsoCat · cited by 2Bicategory.rightUnitorNat…CategoryTheory.Bicategory.associatorNatIsoLeftCat_hom_toNatTrans_app · cited by 0Bicategory.associatorNatI…CategoryTheory.Bicategory.associatorNatIsoLeftCat_inv_toNatTrans_app · cited by 0Bicategory.associatorNatI…CategoryTheory.Bicategory.postcomposingCat_map · cited by 0Bicategory.postcomposingC…CategoryTheory.Bicategory.postcomposingCat_obj · cited by 0Bicategory.postcomposingC…CategoryTheory.Bicategory.associatorNatIsoMiddleCat_hom_toNatTrans_app · cited by 0Bicategory.associatorNatI…CategoryTheory.Bicategory.associatorNatIsoMiddleCat_inv_toNatTrans_app · cited by 0Bicategory.associatorNatI…CategoryTheory.Bicategory.postcomposing₂_map_as_app_toNatTrans_app · cited by 0Bicategory.postcomposing₂…CategoryTheory.Bicategory.postcomposing₂_obj_naturality_hom_toNatTrans_app · cited by 0Bicategory.postcomposing₂…CategoryTheory.Bicategory.postcomposing₂_obj_naturality_inv_toNatTrans_app · cited by 0Bicategory.postcomposing₂…CategoryTheory.Bicategory.postcomp₂_naturality_hom_toNatTrans_app · cited by 0Bicategory.postcomp₂_natu…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.Cat · cited by 884CategoryTheory.CatCategoryTheory.Cat.of · cited by 189Cat.ofCategoryTheory.Functor.toCatHom · cited by 124Functor.toCatHomCategoryTheory.Bicategory.postcomp · cited by 48Bicategory.postcompCategoryTheory.NatTrans.toCatHom₂ · cited by 18NatTrans.toCatHom₂CategoryTheory.Bicategory.postcomposing · cited by 11Bicategory.postcomposingBicategory.postcomposingCatCITED BYCITES

Cites10

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Cited by23

Results whose statement or proof uses this declaration.