Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.HasProduct

{β : Type w} → {C : Type u} → [CategoryTheory.Category.{v, u} C] → (β → C) → Prop

An abbreviation for HasLimit (Discrete.functor f).

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
115 results in Mathlib
Foundations
Depth 13 from the axioms, rests on 71 definitions · uses propext
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.piObj · cited by 237Limits.piObjCategoryTheory.Limits.Pi.π · cited by 184Pi.πCategoryTheory.Limits.Pi.lift · cited by 53Pi.liftCategoryTheory.Limits.Pi.map · cited by 39Pi.mapCategoryTheory.Limits.Pi.hom_ext · cited by 28Pi.hom_extCategoryTheory.Limits.Pi.map' · cited by 20Pi.map'CategoryTheory.Limits.piComparison · cited by 18Limits.piComparisonCategoryTheory.Limits.Pi.map_π · cited by 17Pi.map_πCategoryTheory.Pretriangulated.productTriangle · cited by 15Pretriangulated.productTr…CategoryTheory.Limits.MulticospanIndex.fstPiMap · cited by 14MulticospanIndex.fstPiMapCategoryTheory.Limits.MulticospanIndex.sndPiMap · cited by 14MulticospanIndex.sndPiMapCategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork · cited by 11MulticospanIndex.multifor…CategoryTheory.Limits.productIsProduct · cited by 11Limits.productIsProductCategoryTheory.Limits.piComparison_comp_π · cited by 9Limits.piComparison_comp_πCategoryTheory.Limits.Pi.map'_comp_π · cited by 9Pi.map'_comp_πCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Limits.HasLimit · cited by 226Limits.HasLimitLimits.HasProductCITED BYCITES

Cites3

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

Cited by152

Results whose statement or proof uses this declaration.