Theorems · Definition · category theory

CompHausLike.productIsLimit

{P : TopCat → Prop} →
  (X Y : CompHausLike P) →
    [inst : CompHausLike.HasProp P (↑X.toTop × ↑Y.toTop)] → CategoryTheory.Limits.IsLimit (X.productCone Y)

When the predicate P is preserved under taking type-theoretic products, that product is a category-theoretic product in CompHausLike P.

Defined in: Mathlib.Topology.Category.CompHausLike.Cartesian
Cited by: 0 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompHausLike.HasProp

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Cites17

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

DFunLike.coeproof · cited by 62,936
CategoryTheory.ConcreteCategory.homproof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
CategoryTheory.Discretestatement · cited by 2,447
TopCatstatement and proof · cited by 1,889
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.IsLimitstatement · cited by 664
CategoryTheory.Limits.pairstatement · cited by 536
CompHausLike.toTopstatement and proof · cited by 258
CompHausLikestatement and proof · cited by 145
CategoryTheory.Limits.BinaryFan.sndproof · cited by 53
CategoryTheory.Limits.BinaryFan.fstproof · cited by 53

Cited by1

Results whose statement or proof uses this declaration.

CompHausLike.cartesianMonoidalCategoryproof · cited by 0