Theorems · Definition · category theory
TopCat.generatedBy
{ι : Type t} → (X : ι → Type u) → [(i : ι) → TopologicalSpace (X i)] → CategoryTheory.ObjectProperty TopCatThe property of objects of TopCat which is satisfied by X-generated spaces.
- Defined in
- Mathlib.Topology.Convenient.Category
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- TopCat.carrierproof · cited by 3,184
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.ObjectPropertystatement · cited by 798
- Topology.IsGeneratedByproof · cited by 38
Cited by29
Results whose statement or proof uses this declaration.
- GeneratedByTopCatproof · cited by 10
- ContinuousGeneratedByCat.toGeneratedByTopCatstatement and proof · cited by 5
- ContinuousGeneratedByCat.fromGeneratedByTopCatstatement · cited by 5
- ContinuousGeneratedByCat.equivalencestatement · cited by 4
- GeneratedByTopCat.adjstatement · cited by 2
- TopCat.toGeneratedByTopCatstatement · cited by 2
- GeneratedByTopCat.toTopCatstatement and proof · cited by 2
- GeneratedByTopCat.adjCounitstatement · cited by 1
- GeneratedByTopCat.adjUnitIsostatement · cited by 1
- ContinuousGeneratedByCat.equivalenceCounitIsostatement · cited by 1
- ContinuousGeneratedByCat.equivalenceUnitIsostatement · cited by 1
- ContinuousGeneratedByCat.fromGeneratedByTopCat_objstatement · cited by 0