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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Catstatement · cited by 884
- CategoryTheory.Cat.ofstatement · cited by 189
- CategoryTheory.Functor.toCatHomproof · cited by 124
- CategoryTheory.Bicategory.postcompproof · cited by 48
- CategoryTheory.NatTrans.toCatHom₂proof · cited by 18
- CategoryTheory.Bicategory.postcomposingproof · cited by 11
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.postcomposing₂proof · cited by 10
- CategoryTheory.Bicategory.postcomp₂proof · cited by 6
- CategoryTheory.Bicategory.associatorNatIsoLeftCatstatement · cited by 2
- CategoryTheory.Bicategory.associatorNatIsoMiddleCatstatement · cited by 2
- CategoryTheory.Bicategory.rightUnitorNatIsoCatstatement · cited by 2
- CategoryTheory.Bicategory.associatorNatIsoLeftCat_hom_toNatTrans_appstatement · cited by 0
- CategoryTheory.Bicategory.associatorNatIsoLeftCat_inv_toNatTrans_appstatement · cited by 0
- CategoryTheory.Bicategory.postcomposingCat_mapstatement and proof · cited by 0
- CategoryTheory.Bicategory.postcomposingCat_objstatement and proof · cited by 0
- CategoryTheory.Bicategory.associatorNatIsoMiddleCat_hom_toNatTrans_appstatement · cited by 0
- CategoryTheory.Bicategory.associatorNatIsoMiddleCat_inv_toNatTrans_appstatement · cited by 0
- CategoryTheory.Bicategory.postcomposing₂_map_as_app_toNatTrans_appstatement · cited by 0