Theorems · Definition · category theory

CategoryTheory.Limits.Fork.IsLimit.ofExistsUnique

{C : Type u} →
  {X Y : C} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {f g : X ⟶ Y} →
        {t : CategoryTheory.Limits.Fork f g} →
          (∀ (s : CategoryTheory.Limits.Fork f g), ∃! l, CategoryTheory.CategoryStruct.comp l t.ι = s.ι) →
            CategoryTheory.Limits.IsLimit t

Noncomputably make a limit cone from the existence of unique factorizations.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Equalizers
Cited by: 1 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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 and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.IsLimitstatement · cited by 664
ExistsUniquestatement and proof · cited by 268
CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
CategoryTheory.Limits.Forkstatement and proof · cited by 85
CategoryTheory.Limits.Fork.IsLimit.mkproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3