Theorems · Definition · category theory

CategoryTheory.Limits.Fan.IsLimit.op

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {α : Type u_1} →
      {Z : α → C} →
        {f : CategoryTheory.Limits.Fan Z} → CategoryTheory.Limits.IsLimit f → CategoryTheory.Limits.IsColimit f.op

If a Fan is limit, then its opposite is colimit.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products
Cited by: 1 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites29

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.Functor.objproof · cited by 19,642
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.Isoproof · cited by 3,963
CategoryTheory.Discretestatement and proof · cited by 2,447
CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
CategoryTheory.Equivalence.functorproof · cited by 1,268
CategoryTheory.Equivalence.inverseproof · cited by 1,130
CategoryTheory.Functor.opproof · cited by 997
CategoryTheory.Limits.IsColimitstatement · cited by 773

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.opProductIsoCoproduct'proof · cited by 4
CategoryTheory.Limits.proj_comp_opProductIsoCoproduct'_homproof · cited by 3