Theorems · Definition · category theory
CategoryTheory.Limits.Cofan.inj
{β : Type w} →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {f : β → C} → (p : CategoryTheory.Limits.Cofan f) → (j : β) → f j ⟶ p.ptGet the jth "injection" in the cofan.
(Note that the initial letter of inj matches the greek letter in Cocone.ι.)
- Cited by
- 170 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 126 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.Discrete.functorstatement · cited by 633
- CategoryTheory.Limits.Cocone.ιproof · cited by 605
- CategoryTheory.Limits.Cofanstatement and proof · cited by 124
Cited by222
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimitproof · cited by 29
- CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimitproof · cited by 29
- CategoryTheory.Limits.Cofan.IsColimit.facstatement · cited by 17
- CategoryTheory.SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁proof · cited by 16
- CategoryTheory.Limits.Cofan.IsColimit.hom_extstatement and proof · cited by 16
- CategoryTheory.GradedObject.mapObj_extproof · cited by 14
- HomotopicalAlgebra.AttachCells.reindexproof · cited by 9
- CategoryTheory.PreOneHypercover.sigmaOfIsColimitproof · cited by 6
- CategoryTheory.Limits.Multicofork.ofSigmaCoforkproof · cited by 6
- CategoryTheory.Limits.Cofan.extstatement and proof · cited by 6
- CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_invstatement · cited by 5
- LightCondensed.isoFinYonedaComponentsproof · cited by 5
Showing the 200 most cited of 222.