Theorems · Theorem · category theory

CompHausLike.pullback.condition

∀ {P : TopCat → Prop} {X Y B : CompHausLike P} (f : X ⟶ B) (g : Y ⟶ B) [inst : CompHausLike.HasExplicitPullback f g],
  CategoryTheory.CategoryStruct.comp (CompHausLike.pullback.fst f g) f =
    CategoryTheory.CategoryStruct.comp (CompHausLike.pullback.snd f g) g

Defined in: Mathlib.Topology.Category.CompHausLike.Limits
Cited by: 3 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompHausLike.HasExplicitPullback

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
Set.ofPredproof · cited by 6,101
CategoryTheory.ConcreteCategory.homproof · cited by 4,022
TopCat.carrierproof · cited by 3,184
TopCatstatement and proof · cited by 1,889
CompHausLike.toTopproof · cited by 258
CompHausLikestatement and proof · cited by 145
CategoryTheory.ConcreteCategory.extproof · cited by 107
ContinuousMap.extproof · cited by 92
CompHausLike.HasExplicitPullbackstatement and proof · cited by 14

Cited by4

Results whose statement or proof uses this declaration.

CompHausLike.preregularproof · cited by 19
CompHausLike.pullback.coneproof · cited by 4
CompHausLike.pullback.condition_assocproof · cited by 0
CompHausLike.pullback.cone_πstatement · cited by 0