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 v₁Implementation; see nonempty_indParallelPairPresentation.
- 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Commaproof · cited by 566
- CategoryTheory.Functor.prod'proof · cited by 31
- CategoryTheory.CostructuredArrow.mapproof · cited by 29
- CategoryTheory.Limits.IndObjectPresentationstatement and proof · cited by 20
- CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrowproof · cited by 8
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.NonemptyParallelPairPresentationAux.ι₁statement · cited by 2
- CategoryTheory.NonemptyParallelPairPresentationAux.ι₂statement · cited by 2
- CategoryTheory.NonemptyParallelPairPresentationAux.F₁statement · cited by 2
- CategoryTheory.NonemptyParallelPairPresentationAux.F₂statement · cited by 2
- CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁statement · cited by 2
- CategoryTheory.NonemptyParallelPairPresentationAux.ψstatement and proof · cited by 1
- CategoryTheory.NonemptyParallelPairPresentationAux.ϕstatement and proof · cited by 1
- CategoryTheory.NonemptyParallelPairPresentationAux.presentationproof · cited by 1
- CategoryTheory.NonemptyParallelPairPresentationAux.hfstatement and proof · cited by 0
- CategoryTheory.NonemptyParallelPairPresentationAux.hgstatement and proof · cited by 0
- CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₂statement · cited by 0