Theorems · Definition · category theory
CategoryTheory.Bicategory.LeftExtension
{B : Type u} → [inst : CategoryTheory.Bicategory B] → {a b c : B} → (a ⟶ b) → (a ⟶ c) → Type (max v w)Triangle diagrams for (left) extensions.
``
b
△ \
| \ extension △
f | \ | unit
| ◿
a - - - ▷ c
g
``
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 24 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.
Cites4
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.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.StructuredArrowproof · cited by 370
- CategoryTheory.Bicategory.precompproof · cited by 40
Cited by62
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.LeftExtension.extensionstatement and proof · cited by 19
- CategoryTheory.Bicategory.LeftExtension.whiskerstatement and proof · cited by 15
- CategoryTheory.Bicategory.LeftExtension.unitstatement and proof · cited by 12
- CategoryTheory.Bicategory.lanLeftExtensionstatement and proof · cited by 10
- CategoryTheory.Bicategory.LeftExtension.IsKanstatement and proof · cited by 9
- CategoryTheory.Bicategory.LeftExtension.IsKan.descstatement and proof · cited by 7
- CategoryTheory.Bicategory.LeftExtension.ofCompIdstatement and proof · cited by 6
- CategoryTheory.Bicategory.lanDescstatement and proof · cited by 5
- CategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIsostatement and proof · cited by 3
- CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhiskerstatement · cited by 2
- CategoryTheory.Bicategory.LeftExtension.IsKan.facstatement and proof · cited by 2
- CategoryTheory.Bicategory.LeftExtension.IsKan.ofIsoKanstatement and proof · cited by 2