Theorems · Definition · category theory
CategoryTheory.Limits.HasProducts
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropAn abbreviation for Π J, HasLimitsOfShape (Discrete J) C
- 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.
Cites3
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.Discreteproof · cited by 2,447
- CategoryTheory.Limits.HasLimitsOfShapeproof · cited by 223
Cited by167
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafstatement and proof · cited by 22
- TopCat.Presheaf.SheafConditionEqualizerProducts.diagramstatement and proof · cited by 21
- CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquivstatement and proof · cited by 18
- TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorstatement and proof · cited by 12
- TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInversestatement and proof · cited by 12
- TopCat.Presheaf.SheafConditionEqualizerProducts.piOpensstatement and proof · cited by 11
- TopCat.Presheaf.SheafConditionEqualizerProducts.piIntersstatement and proof · cited by 9
- CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctorstatement and proof · cited by 8
- CategoryTheory.Limits.FormalCoproduct.evalOpstatement and proof · cited by 7
- TopCat.Presheaf.SheafConditionEqualizerProducts.leftResstatement and proof · cited by 7
- TopCat.Presheaf.SheafConditionEqualizerProducts.resstatement and proof · cited by 7
- TopCat.Presheaf.SheafConditionEqualizerProducts.rightResstatement and proof · cited by 7