Theorems · Definition · category theory
CategoryTheory.Limits.parallelPair
{C : Type u} →
{X Y : C} →
[inst : CategoryTheory.Category.{v, u} C] →
(X ⟶ Y) → (X ⟶ Y) → CategoryTheory.Functor CategoryTheory.Limits.WalkingParallelPair CparallelPair f g is the diagram in C consisting of the two morphisms f and g with
common domain and codomain.
- Cited by
- 766 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 79 definitions · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 16,252
- CategoryTheory.Limits.WalkingParallelPairstatement and proof · cited by 781
- CategoryTheory.Limits.parallelPair.parallelPairObjproof · cited by 13
- CategoryTheory.Limits.parallelPair.parallelPairHomproof · cited by 7
Cited by1,282
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.HasKernelproof · cited by 169
- CategoryTheory.Limits.Cofork.πstatement · cited by 164
- CategoryTheory.Limits.Fork.ιstatement · cited by 162
- CategoryTheory.Limits.HasCokernelproof · cited by 131
- CategoryTheory.Limits.coequalizer.πproof · cited by 93
- CategoryTheory.Limits.Forkproof · cited by 85
- CategoryTheory.Limits.Coforkproof · cited by 80
- CategoryTheory.Limits.coequalizerproof · cited by 79
- CategoryTheory.Limits.equalizer.ιproof · cited by 64
- CategoryTheory.Limits.equalizerproof · cited by 60
- CategoryTheory.Limits.HasCoequalizerproof · cited by 54
- CategoryTheory.Limits.kernel.conditionproof · cited by 52
Showing the 200 most cited of 1,282.