Theorems · Definition · category theory
CategoryTheory.Arrow.leftToRight
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Arrow.leftFunc ⟶ CategoryTheory.Arrow.rightFuncThe natural transformation from leftFunc to rightFunc, given by the arrow itself.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 20 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.
Cites7
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 · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.Arrow.homproof · cited by 335
- CategoryTheory.Arrow.leftFuncstatement · cited by 37
- CategoryTheory.Arrow.rightFuncstatement · cited by 32
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.facstatement · cited by 2
- CategoryTheory.Limits.coker.conditionstatement · cited by 1
- CategoryTheory.Arrow.leftToRight_appstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.mk.injstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.mk.noConfusionstatement and proof · cited by 1
- CategoryTheory.Limits.ker.conditionstatement · cited by 1
- CategoryTheory.Limits.cokerIsCokernelstatement · cited by 0
- CategoryTheory.Limits.coker.condition_assocstatement and proof · cited by 0
- CategoryTheory.Limits.kerIsKernelstatement · cited by 0
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assocstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.FunctorialFactorizationData.noConfusionproof · cited by 0