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Theorems · Definition · category theory

CategoryTheory.MonoOver.mapId

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (X : C) →
      CategoryTheory.MonoOver.map (CategoryTheory.CategoryStruct.id X) ≅
        CategoryTheory.Functor.id (CategoryTheory.MonoOver X)

MonoOver.map preserves the identity (up to a natural isomorphism).

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
3 results in Mathlib
Foundations
Depth 33 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.MonoOver.mapIso · cited by 7MonoOver.mapIsoCategoryTheory.MonoOver.mapIso_counitIso · cited by 0MonoOver.mapIso_counitIsoCategoryTheory.Subobject.map_id · cited by 0Subobject.map_idCategoryTheory.MonoOver.mapIso_unitIso · cited by 0MonoOver.mapIso_unitIsoCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.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.trans · cited by 566Iso.transCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Over.isMono · cited by 111Over.isMonoCategoryTheory.MonoOver.map · cited by 12MonoOver.mapCategoryTheory.Over.mapId · cited by 9Over.mapIdCategoryTheory.MonoOver.liftId · cited by 0MonoOver.liftIdCategoryTheory.MonoOver.liftIso · cited by 0MonoOver.liftIsoMonoOver.mapIdCITED BYCITES

Cites13

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

Cited by4

Results whose statement or proof uses this declaration.