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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.pt

Get the jth "injection" in the cofan. (Note that the initial letter of inj matches the greek letter in Cocone.ι.)

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
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.

CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit · cited by 29MultispanIndex.fstSigmaMa…CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit · cited by 29MultispanIndex.sndSigmaMa…CategoryTheory.Limits.Cofan.IsColimit.fac · cited by 17IsColimit.facCategoryTheory.SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ · cited by 16Splitting.toKaroubiNondeg…CategoryTheory.Limits.Cofan.IsColimit.hom_ext · cited by 16IsColimit.hom_extCategoryTheory.GradedObject.mapObj_ext · cited by 14GradedObject.mapObj_extHomotopicalAlgebra.AttachCells.reindex · cited by 9AttachCells.reindexCategoryTheory.PreOneHypercover.sigmaOfIsColimit · cited by 6PreOneHypercover.sigmaOfI…CategoryTheory.Limits.Multicofork.ofSigmaCofork · cited by 6Multicofork.ofSigmaCoforkCategoryTheory.Limits.Cofan.ext · cited by 6Cofan.extCategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv · cited by 5CofanMapObjFun.ιMapObj_is…LightCondensed.isoFinYonedaComponents · cited by 5LightCondensed.isoFinYone…Condensed.isoFinYonedaComponents · cited by 5Condensed.isoFinYonedaCom…CategoryTheory.SimplicialObject.Splitting.hom_ext' · cited by 5Splitting.hom_ext'CategoryTheory.SimplicialObject.Splitting.ι_desc · cited by 5Splitting.ι_descCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.Cocone.pt · cited by 1354Cocone.ptCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Limits.Cocone.ι · cited by 605Cocone.ιCategoryTheory.Limits.Cofan · cited by 124Limits.CofanCofan.injCITED BYCITES

Cites8

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Cited by222

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