Theorems · Definition · category theory
CategoryTheory.Limits.Fork
{C : Type u} → {X Y : C} → [inst : CategoryTheory.Category.{v, u} C] → (X ⟶ Y) → (X ⟶ Y) → Type (max (max 0 u) v)A fork on f and g is just a Cone (parallelPair f g).
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Limits.parallelPairproof · cited by 766
- CategoryTheory.Limits.Coneproof · cited by 710
Cited by188
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
- CategoryTheory.Limits.KernelForkproof · cited by 108
- CategoryTheory.Limits.Fork.ofιstatement · cited by 66
- CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkstatement · cited by 11
- CategoryTheory.Limits.Fork.IsLimit.hom_extstatement and proof · cited by 11
- CategoryTheory.Limits.Fork.conditionstatement and proof · cited by 11
- CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctorstatement and proof · cited by 9
- CategoryTheory.Limits.MulticospanIndex.toPiForkFunctorstatement · cited by 9
- CategoryTheory.Preadditive.forkOfKernelForkstatement · cited by 8
- CategoryTheory.Limits.Fork.IsLimit.lift_ιstatement and proof · cited by 8
- CategoryTheory.Preadditive.kernelForkOfForkstatement and proof · cited by 7
- CategoryTheory.Limits.Fork.extstatement and proof · cited by 7