Theorems · Definition · category theory

CategoryTheory.Limits.IsLimit.liftConeMorphism

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {t : CategoryTheory.Limits.Cone F} →
            CategoryTheory.Limits.IsLimit t → (s : CategoryTheory.Limits.Cone F) → s ⟶ t

The universal morphism from any other cone to a limit cone.

Defined in: Mathlib.CategoryTheory.Limits.IsLimit
Cited by: 18 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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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.Homstatement · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.Conestatement and proof · cited by 710
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.IsLimit.liftproof · cited by 167

Cited by24

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsLimit.ofIsoLimitproof · cited by 39
CategoryTheory.Limits.limit.isoLimitCone_inv_πproof · cited by 26
CategoryTheory.Limits.IsLimit.ofPointIsoproof · cited by 9
CategoryTheory.Limits.limit.isoLimitCone_hom_πproof · cited by 8
CategoryTheory.Limits.IsLimit.uniqueUpToIsoproof · cited by 6
CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_πproof · cited by 5
CategoryTheory.Limits.IsLimit.liftConeMorphism_homstatement and proof · cited by 4
CategoryTheory.Limits.limit.coneMorphismproof · cited by 2
CategoryTheory.Limits.IsLimit.ofRightAdjointproof · cited by 2
CategoryTheory.Limits.IsLimit.uniqueUpToIso_homstatement · cited by 2
CategoryTheory.Limits.Pi.map_eq_prod_mapproof · cited by 1
CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_liftstatement · cited by 1