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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 ``

Defined in
Mathlib.CategoryTheory.Bicategory.Extension
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.

CategoryTheory.Bicategory.LeftExtension.extension · cited by 19LeftExtension.extensionCategoryTheory.Bicategory.LeftExtension.whisker · cited by 15LeftExtension.whiskerCategoryTheory.Bicategory.LeftExtension.unit · cited by 12LeftExtension.unitCategoryTheory.Bicategory.lanLeftExtension · cited by 10Bicategory.lanLeftExtensi…CategoryTheory.Bicategory.LeftExtension.IsKan · cited by 9LeftExtension.IsKanCategoryTheory.Bicategory.LeftExtension.IsKan.desc · cited by 7IsKan.descCategoryTheory.Bicategory.LeftExtension.ofCompId · cited by 6LeftExtension.ofCompIdCategoryTheory.Bicategory.lanDesc · cited by 5Bicategory.lanDescCategoryTheory.Bicategory.LeftExtension.IsKan.uniqueUpToIso · cited by 3IsKan.uniqueUpToIsoCategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker · cited by 2CommuteWith.lanCompIsoWhi…CategoryTheory.Bicategory.LeftExtension.IsKan.fac · cited by 2IsKan.facCategoryTheory.Bicategory.LeftExtension.IsKan.ofIsoKan · cited by 2IsKan.ofIsoKanCategoryTheory.Bicategory.LeftExtension.homMk · cited by 2LeftExtension.homMkCategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf · cited by 2LeftExtension.whiskerOfCo…CategoryTheory.Bicategory.LeftExtension.whiskering · cited by 2LeftExtension.whiskeringQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.StructuredArrow · cited by 370CategoryTheory.Structured…CategoryTheory.Bicategory.precomp · cited by 40Bicategory.precompBicategory.LeftExtensionCITED BYCITES

Cites4

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

Cited by62

Results whose statement or proof uses this declaration.