refactor(Topology/Category): refactor LightProfinite.Basic

[dagurtomas]

This is the second part of the refactor of CompHaus and friends (refactoring the definition of LightProfinite in terms of CompHausLike, see #12930 for the end result)

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• [x] depends on: #13904
• [x] depends on: #13905
• [x] depends on: #13907
• [ ] depends on: #13908
• [ ] depends on: #13909
• [ ] depends on: #13911

[github-actions[bot]]

PR summary 3b9df2fabf

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ instance (X : Type*) [TopologicalSpace X] - LightProfinite - LightProfinite.toCompHaus_comp_toTop - LightProfinite.toTopCat - LightProfinite.toTopCatFullyFaithful - category - coe_comp - coe_id - concreteCategory - hasForget₂ - homeoOfIso - instance : CoeSort LightProfinite (Type*) - instance : LightProfinite.toTopCat.Faithful := LightProfinite.toTopCatFullyFaithful.faithful - instance : LightProfinite.toTopCat.Full := LightProfinite.toTopCatFullyFaithful.full - instance : lightProfiniteToCompHaus.Faithful := lightProfiniteToCompHausFullyFaithful.faithful - instance : lightProfiniteToCompHaus.Full := lightProfiniteToCompHausFullyFaithful.full - instance : lightToProfinite.Faithful := lightToProfiniteFullyFaithful.faithful - instance : lightToProfinite.Full := lightToProfiniteFullyFaithful.full - instance {X : LightProfinite} : CompactSpace ((forget LightProfinite).obj X) - instance {X : LightProfinite} : SecondCountableTopology (lightProfiniteToCompHaus.obj X) - instance {X : LightProfinite} : T2Space ((forget LightProfinite).obj X) - instance {X : LightProfinite} : TopologicalSpace ((forget LightProfinite).obj X) - instance {X : LightProfinite} : TotallyDisconnectedSpace (lightProfiniteToCompHaus.obj X) - instance {X Y : LightProfinite} (f : X ⟶ Y) [@Epi CompHaus _ _ _ f] : Epi f := by - instance {X Y : LightProfinite} (f : X ⟶ Y) [Epi f] : @Epi CompHaus _ _ _ f := by - isoEquivHomeo - isoOfHomeo - lightProfiniteToCompHaus - lightProfiniteToCompHausFullyFaithful - lightToProfinite - lightToProfiniteFullyFaithful - mono_iff_injective - of

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for `script/declarations_diff.sh` contains some details about this script.

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#13904~~
• ~~leanprover-community/mathlib4#13905~~
• ~~leanprover-community/mathlib4#13907~~
• ~~leanprover-community/mathlib4#13908~~
• ~~leanprover-community/mathlib4#13909~~ By Dependent Issues (🤖). Happy coding!

[mathlib-bors[bot]]

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