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Theorems · Definition · category theory

CategoryTheory.CatEnrichedOrdinary.Hom.base

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.EnrichedOrdinaryCategory CategoryTheory.Cat C] →
      {X Y : CategoryTheory.CatEnrichedOrdinary C} →
        {f g : X ⟶ Y} →
          (f ⟶ g) → (CategoryTheory.CatEnrichedOrdinary.homEquiv f ⟶ CategoryTheory.CatEnrichedOrdinary.homEquiv g)

A 2-cell in CatEnrichedOrdinary C has a corresponding "base" 2-cell in CatEnriched C.

Defined in
Mathlib.CategoryTheory.Bicategory.CatEnriched
Cited by
12 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory

Around this declaration

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

CategoryTheory.CatEnrichedOrdinary.hComp · cited by 9CatEnrichedOrdinary.hCompCategoryTheory.CatEnrichedOrdinary.Hom.ext · cited by 4Hom.extCategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom · cited by 3Hom.base_eqToHomCategoryTheory.CatEnrichedOrdinary.hComp_assoc · cited by 1CatEnrichedOrdinary.hComp…CategoryTheory.CatEnrichedOrdinary.hComp_id · cited by 1CatEnrichedOrdinary.hComp…CategoryTheory.CatEnrichedOrdinary.id_hComp · cited by 1CatEnrichedOrdinary.id_hC…CategoryTheory.CatEnrichedOrdinary.base_mk · cited by 0CatEnrichedOrdinary.base_…CategoryTheory.CatEnrichedOrdinary.hComp_comp · cited by 0CatEnrichedOrdinary.hComp…CategoryTheory.CatEnrichedOrdinary.Hom.base_comp · cited by 0Hom.base_compCategoryTheory.CatEnrichedOrdinary.Hom.base_id · cited by 0Hom.base_idCategoryTheory.CatEnrichedOrdinary.Hom.comp_eq · cited by 0Hom.comp_eqCategoryTheory.CatEnrichedOrdinary.Hom.ext_iff · cited by 0Hom.ext_iffCategoryTheory.CatEnrichedOrdinary.mk_base · cited by 0CatEnrichedOrdinary.mk_ba…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomEquiv · cited by 8337EquivCategoryTheory.Cat · cited by 884CategoryTheory.CatCategoryTheory.EnrichedOrdinaryCategory · cited by 109CategoryTheory.EnrichedOr…CategoryTheory.CatEnriched · cited by 25CategoryTheory.CatEnrichedCategoryTheory.CatEnrichedOrdinary · cited by 24CategoryTheory.CatEnriche…CategoryTheory.CatEnrichedOrdinary.homEquiv · cited by 18CatEnrichedOrdinary.homEq…CategoryTheory.CatEnrichedOrdinary.toBase · cited by 16CatEnrichedOrdinary.toBaseCategoryTheory.CatEnrichedOrdinary.Hom.base' · cited by 0Hom.base'Hom.baseCITED BYCITES

Cites11

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Cited by13

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