Theorems · Theorem · category theory

CategoryTheory.Limits.PullbackCone.condition

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  (t : CategoryTheory.Limits.PullbackCone f g),
  CategoryTheory.CategoryStruct.comp t.fst f = CategoryTheory.CategoryStruct.comp t.snd g

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 44 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites13

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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136
CategoryTheory.Limits.PullbackCone.fststatement · cited by 118
CategoryTheory.Limits.PullbackCone.sndstatement · cited by 113
CategoryTheory.Limits.Cone.wproof · cited by 40
CategoryTheory.Limits.WalkingCospan.Hom.inlproof · cited by 24

Cited by51

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pullback.conditionproof · cited by 122
CategoryTheory.IsPullback.of_isLimitproof · cited by 12
CategoryTheory.regularTopology.equalizerCondition_wproof · cited by 7
CategoryTheory.Limits.PullbackCone.etastatement · cited by 5
CategoryTheory.Limits.PullbackCone.condition_assocproof · cited by 4
CategoryTheory.IsPullback.of_horiz_isIso_monoproof · cited by 4
AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMapproof · cited by 4
CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_leftproof · cited by 3
CategoryTheory.Limits.PullbackCone.fst_eq_snd_of_mono_eqproof · cited by 3
CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_rightproof · cited by 2
CategoryTheory.IsPullback.mk'proof · cited by 2
CategoryTheory.mono_iff_fst_eq_sndproof · cited by 2