Theorems · Inductive type · category theory
CategoryTheory.Limits.HasCountableProducts
(C : Type u_1) → [CategoryTheory.Category.{v_1, u_1} C] → PropA category has countable products if it has all products indexed by countable types.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.SequentialProduct.functorMapstatement and proof · cited by 9
- CategoryTheory.Limits.SequentialProduct.functorObjstatement and proof · cited by 9
- CategoryTheory.Limits.SequentialProduct.conestatement and proof · cited by 5
- CategoryTheory.CountableAB4Starstatement · cited by 3
- CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat_and_finitestatement and proof · cited by 1
- CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_negstatement and proof · cited by 1
- CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_posstatement and proof · cited by 1
- CategoryTheory.Limits.SequentialProduct.functorMap_commSq_auxstatement and proof · cited by 1
- CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succstatement and proof · cited by 1
- CategoryTheory.CountableAB4Star.casesOnstatement and proof · cited by 0
- CategoryTheory.Limits.HasCountableProducts.casesOnstatement and proof · cited by 0
- CategoryTheory.Limits.HasCountableProducts.outstatement and proof · cited by 0