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Theorems · Definition · category theory

CategoryTheory.EnrichedCategory.id

{V : Type v} →
  {inst : CategoryTheory.Category.{w, v} V} →
    {inst_1 : CategoryTheory.MonoidalCategory V} →
      {C : Type u₁} →
        [self : CategoryTheory.EnrichedCategory V C] →
          (X : C) → CategoryTheory.MonoidalCategoryStruct.tensorUnit V ⟶ X ⟶[V] X

The identity morphism of this category

Defined in
Mathlib.CategoryTheory.Enriched.Basic
Cited by
3 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.EnrichedCategory
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Around this declaration

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

CategoryTheory.eId · cited by 25CategoryTheory.eIdCategoryTheory.EnrichedCategory.comp_id · cited by 1EnrichedCategory.comp_idCategoryTheory.EnrichedCategory.id_comp · cited by 1EnrichedCategory.id_compCategoryTheory.SimplicialThickening.id_app · cited by 0SimplicialThickening.id_a…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.EnrichedCategory.Hom · cited by 114EnrichedCategory.HomCategoryTheory.EnrichedCategory · cited by 99CategoryTheory.EnrichedCa…EnrichedCategory.idCITED BYCITES

Cites6

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.