Theorems · Definition · category theory

CompHaus.limitConeIsLimit

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    (F : CategoryTheory.Functor J CompHaus) → CategoryTheory.Limits.IsLimit (CompHaus.limitCone F)

The limit cone CompHaus.limitCone F is indeed a limit cone.

Defined in: Mathlib.Topology.Category.CompHaus.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory

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Cites13

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

CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compproof · cited by 6,529
TopCatstatement · cited by 1,889
CategoryTheory.Limits.Coneproof · cited by 710
CategoryTheory.Limits.IsLimitstatement · cited by 664
CategoryTheory.SmallCategorystatement and proof · cited by 480
CategoryTheory.Limits.IsLimit.liftproof · cited by 167
CategoryTheory.Functor.mapConeproof · cited by 147
CompHausstatement and proof · cited by 61
CategoryTheory.InducedCategory.homMkproof · cited by 33
TopCat.limitConeIsLimitproof · cited by 1
CompHaus.limitConestatement · cited by 0

Cited by2

Results whose statement or proof uses this declaration.

LightProfinite.limitConeIsLimitproof · cited by 0
Profinite.limitConeIsLimitproof · cited by 0