Theorems · Definition · category theory
ContinuousGeneratedByCat.equivalence
{ι : Type t} →
{X : ι → Type u} → [inst : (i : ι) → TopologicalSpace (X i)] → GeneratedByTopCat X ≌ ContinuousGeneratedByCat XThe equivalence of categories GeneratedByTopCat X ≌ ContinuousGeneratedByCat X.
- Defined in
- Mathlib.Topology.Convenient.Category
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- TopCatstatement · cited by 1,889
- CategoryTheory.Equivalencestatement · cited by 601
- ContinuousGeneratedByCatstatement · cited by 23
- TopCat.generatedBystatement · cited by 11
- GeneratedByTopCatstatement · cited by 10
- ContinuousGeneratedByCat.toGeneratedByTopCatproof · cited by 5
- ContinuousGeneratedByCat.fromGeneratedByTopCatproof · cited by 5
- ContinuousGeneratedByCat.equivalenceCounitIsoproof · cited by 1
- ContinuousGeneratedByCat.equivalenceUnitIsoproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousGeneratedByCat.equivalence_counitIsostatement and proof · cited by 0
- ContinuousGeneratedByCat.equivalence_functorstatement and proof · cited by 0
- ContinuousGeneratedByCat.equivalence_inversestatement and proof · cited by 0
- ContinuousGeneratedByCat.equivalence_unitIsostatement and proof · cited by 0