Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.HasProducts

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

An abbreviation for Π J, HasLimitsOfShape (Discrete J) C

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
103 results in Mathlib
Foundations
Depth 11 from the axioms, rests on 60 definitions · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.GrothendieckTopology.Point.skyscraperPresheaf · cited by 22Point.skyscraperPresheafTopCat.Presheaf.SheafConditionEqualizerProducts.diagram · cited by 21SheafConditionEqualizerPr…CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv · cited by 18Point.skyscraperPresheafH…TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor · cited by 12SheafConditionPairwiseInt…TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse · cited by 12SheafConditionPairwiseInt…TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens · cited by 11SheafConditionEqualizerPr…TopCat.Presheaf.SheafConditionEqualizerProducts.piInters · cited by 9SheafConditionEqualizerPr…CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctor · cited by 8Point.skyscraperPresheafF…CategoryTheory.Limits.FormalCoproduct.evalOp · cited by 7FormalCoproduct.evalOpTopCat.Presheaf.SheafConditionEqualizerProducts.leftRes · cited by 7SheafConditionEqualizerPr…TopCat.Presheaf.SheafConditionEqualizerProducts.res · cited by 7SheafConditionEqualizerPr…TopCat.Presheaf.SheafConditionEqualizerProducts.rightRes · cited by 7SheafConditionEqualizerPr…CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor · cited by 7Point.skyscraperSheafFunc…CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor · cited by 5FormalCoproduct.cosimplic…CategoryTheory.Limits.piFunctor · cited by 5Limits.piFunctorCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.HasLimitsOfShape · cited by 223Limits.HasLimitsOfShapeLimits.HasProductsCITED BYCITES

Cites3

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

Cited by167

Results whose statement or proof uses this declaration.