Theorems · Definition · category theory
CategoryTheory.Limits.HasBinaryProducts
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category HasBinaryProducts if it has all limits of shape Discrete WalkingPair,
i.e. if it has a product for every pair of objects.
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.WalkingPairproof · cited by 1,319
- CategoryTheory.Limits.HasLimitsOfShapeproof · cited by 223
Cited by104
Results whose statement or proof uses this declaration.
- CategoryTheory.prodComonadstatement and proof · cited by 20
- CategoryTheory.Limits.prod.functorstatement and proof · cited by 14
- CategoryTheory.Over.starstatement and proof · cited by 8
- CategoryTheory.overToCoalgebrastatement and proof · cited by 8
- CategoryTheory.coalgebraToOverstatement and proof · cited by 8
- CategoryTheory.Limits.prod.associatorstatement and proof · cited by 7
- SheafOfModules.Presentation.quasicoherentDatastatement and proof · cited by 4
- CategoryTheory.coalgebraEquivOverstatement and proof · cited by 4
- SheafOfModules.GeneratingSections.localGeneratorsDatastatement and proof · cited by 3
- CategoryTheory.ProdPreservesConnectedLimits.forgetConestatement and proof · cited by 3
- CategoryTheory.Limits.prod.associator_homstatement and proof · cited by 3
- CategoryTheory.Limits.prodComparisonNatTransstatement and proof · cited by 3