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Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.eqToHom_left

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {T : D} {S : CategoryTheory.Functor C D} {X Y : CategoryTheory.CostructuredArrow S T} (h : X = Y),
  (CategoryTheory.eqToHom h).left = CategoryTheory.eqToHom ⋯
Defined in
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
Cited by
10 results in Mathlib
Foundations
Depth 25 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.homMk'_comp · cited by 1CostructuredArrow.homMk'_…CategoryTheory.CostructuredArrow.homMk'_id · cited by 1CostructuredArrow.homMk'_…CategoryTheory.CostructuredArrow.mkPrecomp_comp · cited by 1CostructuredArrow.mkPreco…CategoryTheory.CostructuredArrow.mkPrecomp_id · cited by 1CostructuredArrow.mkPreco…CategoryTheory.OverPresheafAux.unitBackward_unitForward · cited by 0OverPresheafAux.unitBackw…CategoryTheory.OverPresheafAux.unitForward_naturality₁ · cited by 0OverPresheafAux.unitForwa…CategoryTheory.OverPresheafAux.unitForward_naturality₂ · cited by 0OverPresheafAux.unitForwa…CategoryTheory.OverPresheafAux.unitForward_unitBackward · cited by 0OverPresheafAux.unitForwa…CategoryTheory.OverPresheafAux.counitForward_naturality₂ · cited by 0OverPresheafAux.counitFor…CategoryTheory.CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality · cited by 0CategoryOfElements.costru…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.eqToHom · cited by 860CategoryTheory.eqToHomCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CategoryTheory.CommaMorphism.left · cited by 526CommaMorphism.leftCategoryTheory.CostructuredArrow.left · cited by 202CostructuredArrow.leftCostructuredArrow.eqToHom_leftCITED BYCITES

Cites11

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Cited by10

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