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Theorems · Definition · category theory

CategoryTheory.Over.mapId

{T : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} T] →
    (Y : T) →
      CategoryTheory.Over.map (CategoryTheory.CategoryStruct.id Y) ≅ CategoryTheory.Functor.id (CategoryTheory.Over Y)

The natural isomorphism arising from mapForget_eq.

Defined in
Mathlib.CategoryTheory.Comma.Over.Basic
Cited by
9 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ChosenPullbacksAlong.id · cited by 6ChosenPullbacksAlong.idCategoryTheory.GrothendieckTopology.overMapPullbackId · cited by 6GrothendieckTopology.over…CategoryTheory.MonoOver.mapId · cited by 3MonoOver.mapIdCategoryTheory.GrothendieckTopology.overMapPullbackId_hom_app_hom_app · cited by 2GrothendieckTopology.over…CategoryTheory.GrothendieckTopology.overMapPullback_comp_id · cited by 1GrothendieckTopology.over…CategoryTheory.GrothendieckTopology.overMapPullback_id_comp · cited by 1GrothendieckTopology.over…CategoryTheory.Over.mapId_eq · cited by 0Over.mapId_eqCategoryTheory.Over.mapId_hom_app_left · cited by 0Over.mapId_hom_app_leftCategoryTheory.Over.mapId_inv_app_left · cited by 0Over.mapId_inv_app_leftCategoryTheory.Over.pullbackId · cited by 0Over.pullbackIdCategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_hom_app · cited by 0GrothendieckTopology.pseu…CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_hom_app · cited by 0GrothendieckTopology.pseu…CategoryTheory.GrothendieckTopology.overMapPullbackId_inv_app_hom_app · cited by 0GrothendieckTopology.over…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Over.left · cited by 541Over.leftCategoryTheory.NatIso.ofComponents · cited by 178NatIso.ofComponentsCategoryTheory.Over.map · cited by 97Over.mapCategoryTheory.Over.isoMk · cited by 22Over.isoMkOver.mapIdCITED BYCITES

Cites12

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

Cited by13

Results whose statement or proof uses this declaration.