Theorems · Theorem · category theory
CategoryTheory.Limits.Fork.condition
∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] {f g : X ⟶ Y} (t : CategoryTheory.Limits.Fork f g),
CategoryTheory.CategoryStruct.comp t.ι f = CategoryTheory.CategoryStruct.comp t.ι g- Cited by
- 11 results in Mathlib
- Foundations
- Depth 26 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.
Cites14
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.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.Limits.WalkingParallelPairstatement and proof · cited by 781
- CategoryTheory.Limits.parallelPairstatement and proof · cited by 766
- CategoryTheory.Limits.Cone.πproof · cited by 500
- CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
- CategoryTheory.Limits.Forkstatement and proof · cited by 85
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.equalizer.conditionproof · cited by 16
- CategoryTheory.Limits.KernelFork.conditionproof · cited by 7
- CategoryTheory.Limits.Fork.isoForkOfιstatement · cited by 3
- CategoryTheory.Limits.weakEqualizer.conditionproof · cited by 3
- CategoryTheory.Functor.preservesEqualizer_of_preservesKernelsproof · cited by 1
- CategoryTheory.Limits.isoOfιstatement · cited by 0
- CategoryTheory.IsPullback.isLimitForkproof · cited by 0
- CategoryTheory.Limits.eq_of_epi_fork_ιproof · cited by 0
- CategoryTheory.Limits.Fork.condition_assocproof · cited by 0
- CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epiproof · cited by 0
- CategoryTheory.Limits.Fork.isoForkOfι_hom_homstatement · cited by 0