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Theorems · Definition · category theory

CategoryTheory.NonemptyParallelPairPresentationAux.K

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} →
      (A ⟶ B) →
        (A ⟶ B) →
          CategoryTheory.Limits.IndObjectPresentation A → CategoryTheory.Limits.IndObjectPresentation B → Type v₁

Implementation; see nonempty_indParallelPairPresentation.

Defined in
Mathlib.CategoryTheory.Limits.Indization.ParallelPair
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.NonemptyParallelPairPresentationAux.ι₁ · cited by 2NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.ι₂ · cited by 2NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.F₁ · cited by 2NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.F₂ · cited by 2NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁ · cited by 2NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.ψ · cited by 1NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.ϕ · cited by 1NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.presentation · cited by 1NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.hf · cited by 0NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.hg · cited by 0NonemptyParallelPairPrese…CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₂ · cited by 0NonemptyParallelPairPrese…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Comma · cited by 566CategoryTheory.CommaCategoryTheory.Functor.prod' · cited by 31Functor.prod'CategoryTheory.CostructuredArrow.map · cited by 29CostructuredArrow.mapCategoryTheory.Limits.IndObjectPresentation · cited by 20Limits.IndObjectPresentat…CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow · cited by 8IndObjectPresentation.toC…NonemptyParallelPairPresentat…CITED BYCITES

Cites10

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Cited by11

Results whose statement or proof uses this declaration.