Theorems · Definition · category theory

CategoryTheory.Limits.lim

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [CategoryTheory.Limits.HasLimitsOfShape J C] → CategoryTheory.Functor (CategoryTheory.Functor J C) C

limit F is functorial in F, when C has all limits of shape J.

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 70 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasLimitsOfShape

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

Cites6

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.Homproof · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.limitproof · cited by 346
CategoryTheory.Limits.HasLimitsOfShapestatement and proof · cited by 223
CategoryTheory.Limits.limMapproof · cited by 29

Cited by105

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.limitUncurryIsoLimitCompLimstatement and proof · cited by 7
CategoryTheory.preservesLimitNatIsostatement · cited by 6
CategoryTheory.Limits.Pi.mapIsoproof · cited by 6
CategoryTheory.Limits.limitIsoLimitCurryCompLimstatement and proof · cited by 6
CategoryTheory.Limits.colimitLimitToLimitColimitstatement and proof · cited by 6
CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_πstatement and proof · cited by 5
CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLimstatement and proof · cited by 4
CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLimstatement · cited by 4
CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_πstatement and proof · cited by 4
CategoryTheory.Limits.ι_colimitLimitToLimitColimit_πstatement and proof · cited by 3
CategoryTheory.Limits.DiagramOfCones.mkOfHasLimitsproof · cited by 3
CategoryTheory.Limits.limitIsoLimitCurryCompLim_inv_πstatement and proof · cited by 3