Mathlib Map

Theorems · Inductive type · category theory

CategoryTheory.Limits.HasCountableProducts

(C : Type u_1) → [CategoryTheory.Category.{v_1, u_1} C] → Prop

A category has countable products if it has all products indexed by countable types.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Countable
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.

CategoryTheory.Limits.SequentialProduct.functorMap · cited by 9SequentialProduct.functor…CategoryTheory.Limits.SequentialProduct.functorObj · cited by 9SequentialProduct.functor…CategoryTheory.Limits.SequentialProduct.cone · cited by 5SequentialProduct.coneCategoryTheory.CountableAB4Star · cited by 3CategoryTheory.CountableA…CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat_and_finite · cited by 1CountableAB4Star.of_hasEx…CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_neg · cited by 1SequentialProduct.cone_π_…CategoryTheory.Limits.SequentialProduct.cone_π_app_comp_Pi_π_pos · cited by 1SequentialProduct.cone_π_…CategoryTheory.Limits.SequentialProduct.functorMap_commSq_aux · cited by 1SequentialProduct.functor…CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ · cited by 1SequentialProduct.functor…CategoryTheory.CountableAB4Star.casesOn · cited by 0CountableAB4Star.casesOnCategoryTheory.Limits.HasCountableProducts.casesOn · cited by 0HasCountableProducts.case…CategoryTheory.Limits.HasCountableProducts.out · cited by 0HasCountableProducts.outCategoryTheory.CountableAB4Star.of_countableAB5Star · cited by 0CountableAB4Star.of_count…CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat · cited by 0CountableAB4Star.of_hasEx…CategoryTheory.Limits.HasCountableProducts.recOn · cited by 0HasCountableProducts.recOnCategoryTheory.Category · cited by 32673CategoryTheory.CategoryLimits.HasCountableProductsCITED BYCITES

Cites1

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

Cited by24

Results whose statement or proof uses this declaration.