Theorems · Definition · category theory

CategoryTheory.Limits.limit

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

An arbitrary choice of limit object of a functor.

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 346 results in Mathlib
Foundations: Depth 6 from the axioms, rests on 11 definitions · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasLimit

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Cites5

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
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.Cone.ptproof · cited by 1,298
CategoryTheory.Limits.HasLimitstatement and proof · cited by 226
CategoryTheory.Limits.limit.coneproof · cited by 97

Cited by455

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pullbackproof · cited by 864
CategoryTheory.Limits.prodproof · cited by 364
CategoryTheory.Limits.limit.πstatement · cited by 278
CategoryTheory.Limits.limit.lift_πstatement · cited by 266
CategoryTheory.Limits.piObjproof · cited by 237
CategoryTheory.Limits.terminalproof · cited by 141
CategoryTheory.Limits.limit.lift_π_assocstatement · cited by 95
CategoryTheory.Limits.limproof · cited by 70
CategoryTheory.Limits.equalizerproof · cited by 60
CategoryTheory.Limits.limit.liftstatement · cited by 48
CategoryTheory.Limits.HasLimit.isoOfNatIsostatement · cited by 41
CategoryTheory.Limits.limitObjIsoLimitCompEvaluationstatement · cited by 36

Showing the 200 most cited of 455.