Theorems · Definition · category theory
ContinuousGeneratedByCat.adjUnitIso
{ι : Type t} →
{X : ι → Type u} →
[inst : (i : ι) → TopologicalSpace (X i)] →
CategoryTheory.Functor.id (ContinuousGeneratedByCat X) ≅
(ContinuousGeneratedByCat.toTopCat X).comp (TopCat.toContinuousGeneratedByCat X)The unit (isomorphism) of the adjunction ContinuousGeneratedByCat.adj between
the categories ContinuousGeneratedByCat X and TopCat.
- Defined in
- Mathlib.Topology.Convenient.Category
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 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.
Cites13
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
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- TopCatstatement · cited by 1,889
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- ContinuousGeneratedByCatstatement and proof · cited by 23
- ContinuousGeneratedByCat.carrierproof · cited by 14
- ContinuousGeneratedByCat.toTopCatstatement · cited by 4
- TopCat.toContinuousGeneratedByCatstatement · cited by 2
- Topology.WithGeneratedByTopology.equivAsContinuousMapGeneratedByproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousGeneratedByCat.adjproof · cited by 2
- ContinuousGeneratedByCat.equivalenceCounitIsoproof · cited by 1
- ContinuousGeneratedByCat.adj_unitstatement · cited by 0