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Theorems · Definition · category theory

CategoryTheory.Limits.HasProductsOfShape

Type v → (C : Type u_1) → [CategoryTheory.Category.{u_2, u_1} C] → Prop

An abbreviation for HasLimitsOfShape (Discrete f).

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
63 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.FormalCoproduct.power · cited by 27FormalCoproduct.powerCategoryTheory.Limits.pointwiseProduct · cited by 14Limits.pointwiseProductCategoryTheory.Limits.Pi.functor · cited by 13Pi.functorCategoryTheory.Limits.FormalCoproduct.mapPower · cited by 11FormalCoproduct.mapPowerCategoryTheory.Limits.FormalCoproduct.powerMap · cited by 9FormalCoproduct.powerMapCategoryTheory.Limits.FormalCoproduct.powerπ · cited by 8FormalCoproduct.powerπCategoryTheory.Limits.IsIPCOfShape · cited by 6Limits.IsIPCOfShapeCategoryTheory.Limits.coconePointwiseProduct · cited by 6Limits.coconePointwisePro…CategoryTheory.evaluationRightAdjoint · cited by 6CategoryTheory.evaluation…CategoryTheory.Limits.Pi.mapIso · cited by 6Pi.mapIsoCategoryTheory.Limits.colimitPointwiseProductToProductColimit · cited by 6Limits.colimitPointwisePr…CategoryTheory.Limits.FormalCoproduct.powerFunctor · cited by 5FormalCoproduct.powerFunc…CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompLim · cited by 4Limits.piEquivalenceFunct…CategoryTheory.Limits.ι_colimitPointwiseProductToProductColimit_π · cited by 3Limits.ι_colimitPointwise…CategoryTheory.Limits.Pi.constCompPiIsoConst · cited by 3Pi.constCompPiIsoConstCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.HasLimitsOfShape · cited by 223Limits.HasLimitsOfShapeLimits.HasProductsOfShapeCITED BYCITES

Cites3

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

Cited by91

Results whose statement or proof uses this declaration.