Theorems · Definition · category theory
CategoryTheory.Bicategory.precomp
{B : Type u} →
[inst : CategoryTheory.Bicategory B] → {a b : B} → (c : B) → (a ⟶ b) → CategoryTheory.Functor (b ⟶ c) (a ⟶ c)Precomposition of a 1-morphism as a functor.
- Defined in
- Mathlib.CategoryTheory.Bicategory.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- CategoryTheory.Bicategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Bicategory.whiskerLeftproof · cited by 524
Cited by59
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.LeftExtensionproof · cited by 29
- CategoryTheory.Bicategory.precomposingCatproof · cited by 24
- CategoryTheory.Bicategory.precomposingproof · cited by 11
- CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIsostatement · cited by 3
- CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelfstatement · cited by 2
- CategoryTheory.Bicategory.LeftExtension.whiskeringstatement · cited by 2
- CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhiskerstatement · cited by 2
- CategoryTheory.Bicategory.LeftExtension.IsKan.ofIsoKanstatement · cited by 2
- CategoryTheory.Bicategory.RightExtensionproof · cited by 2
- CategoryTheory.Bicategory.LeftExtension.homMkstatement · cited by 2
- CategoryTheory.Bicategory.RightExtension.wstatement · cited by 1
- CategoryTheory.Bicategory.LeftExtension.IsAbsKan.ofIsoAbsKanstatement · cited by 1