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Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.w

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {S : CategoryTheory.Functor C D} {T : D} {X Y : CategoryTheory.CostructuredArrow S T} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (S.map f.left) Y.hom = X.hom
Defined in
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
Cited by
10 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.CostructuredArrow.Hom.w · cited by 1Hom.wCategoryTheory.Bicategory.RightLift.w · cited by 1RightLift.wCategoryTheory.CostructuredArrow.homMk_surjective · cited by 1CostructuredArrow.homMk_s…CategoryTheory.CostructuredArrow.w_prod_fst · cited by 1CostructuredArrow.w_prod_…CategoryTheory.CostructuredArrow.w_prod_snd · cited by 1CostructuredArrow.w_prod_…CategoryTheory.exists_eq_of_isCofiltered_costructuredArrow · cited by 1CategoryTheory.exists_eq_…CategoryTheory.Functor.bijective_sectionsPrecomp · cited by 1Functor.bijective_section…CategoryTheory.Bicategory.RightExtension.w · cited by 1RightExtension.wCategoryTheory.CostructuredArrow.w_assoc · cited by 0CostructuredArrow.w_assocCategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.hom_ext · cited by 0IsPointwiseRightKanExtens…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CategoryTheory.CommaMorphism.left · cited by 526CommaMorphism.leftCategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.CostructuredArrow.hom · cited by 179CostructuredArrow.homCategoryTheory.CommaMorphism.w · cited by 24CommaMorphism.wCostructuredArrow.wCITED BYCITES

Cites15

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Cited by10

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