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Theorems · Definition · category theory

CategoryTheory.Limits.Pi.functor

(α : Type w₂) →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [CategoryTheory.Limits.HasProductsOfShape α C] → CategoryTheory.Functor (α → C) C

The functor (f : α → C) ↦ ∏ᶜ f.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
13 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasProductsOfShape

Around this declaration

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

CategoryTheory.Limits.pointwiseProduct · cited by 14Limits.pointwiseProductCategoryTheory.Limits.colimitPointwiseProductToProductColimit · cited by 6Limits.colimitPointwisePr…CategoryTheory.Limits.coconePointwiseProduct · cited by 6Limits.coconePointwisePro…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim · cited by 4Limits.piEquivalenceFunct…CategoryTheory.Limits.Pi.constCompPiIsoConst · cited by 3Pi.constCompPiIsoConstCategoryTheory.Limits.Pi.functorπ · cited by 3Pi.functorπCategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π_assoc · cited by 1Limits.ι_colimitPointwise…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim_comp_functorπ · cited by 1Limits.piEquivalenceFunct…CategoryTheory.Limits.colimitPointwiseProductToProductColimit_app · cited by 0Limits.colimitPointwisePr…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim_comp_functorπ_assoc · cited by 0Limits.piEquivalenceFunct…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim_hom_app · cited by 0Limits.piEquivalenceFunct…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim_inv_app · cited by 0Limits.piEquivalenceFunct…CategoryTheory.Limits.Types.isIso_colimitPointwiseProductToProductColimit · cited by 0Types.isIso_colimitPointw…CategoryTheory.Limits.coconePointwiseProduct_ι · cited by 0Limits.coconePointwisePro…CategoryTheory.Limits.Pi.constCompPiIsoConst_hom_app · cited by 0Pi.constCompPiIsoConst_ho…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Limits.piObj · cited by 237Limits.piObjCategoryTheory.Limits.HasProductsOfShape · cited by 63Limits.HasProductsOfShapeCategoryTheory.Limits.Pi.map · cited by 39Pi.mapPi.functorCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.