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[Merged by Bors] - feat(Topology/CompHaus): sigma-comparison map#15525

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[Merged by Bors] - feat(Topology/CompHaus): sigma-comparison map#15525
dagurtomas wants to merge 9 commits intomasterfrom
dagur/SigmaComparison

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@dagurtomas dagurtomas commented Aug 5, 2024 •
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This PR defines the map CompHausLike.sigmaComparison associated to a presheaf X on
CompHausLike P, and a finite family S₁,...,Sₙ of spaces in CompHausLike P, where P is
stable under taking finite disjoint unions.

The map sigmaComparison is the canonical map X(S₁ ⊔ ... ⊔ Sₙ) ⟶ X(S₁) × ... × X(Sₙ) induced by
the inclusion maps Sᵢ ⟶ S₁ ⊔ ... ⊔ Sₙ, and it is an isomorphism when X preserves finite
products.

This is useful when proving that discrete condensed sets are given by locally constant maps, see #15321

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@dagurtomas dagurtomas added t-category-theory Category theory t-topology Topological spaces, uniform spaces, metric spaces, filters labels Aug 5, 2024
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github-actions bot commented Aug 5, 2024 •
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PR summary 001476a96c

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Topology.Category.CompHausLike.SigmaComparison 817

Declarations diff

+ instance : HasProp P (Σ (a : α), (σ a)) := HasExplicitFiniteCoproducts.hasProp (fun a ↦ of P (σ a))
+ instance : PreservesLimitsOfShape (Discrete α) X
+ isIsoSigmaComparison
+ sigmaComparison
+ sigmaComparison_eq_comp_isos

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.

@dagurtomas dagurtomas mentioned this pull request Aug 5, 2024
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callesonne
callesonne reviewed Aug 27, 2024
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@callesonne callesonne added the awaiting-author A reviewer has asked the author a question or requested changes. label Aug 27, 2024
@dagurtomas dagurtomas force-pushed the dagur/SigmaComparison branch from 72afe71 to 2fe0c7f Compare August 27, 2024 12:20
@dagurtomas dagurtomas removed the awaiting-author A reviewer has asked the author a question or requested changes. label Aug 27, 2024
@ghost ghost added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 27, 2024
@ghost ghost removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 27, 2024
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ghost commented Aug 27, 2024

This PR/issue depends on:

callesonne
callesonne approved these changes Aug 27, 2024
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Have I understood correctly that these theorems should fit into some quite general API about HasExplicit(Co)Products and PreservesExplicit(Co)Products (although that is of course out of the scope of this PR)? LGTM!

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dagurtomas commented Aug 27, 2024

Have I understood correctly that these theorems should fit into some quite general API about HasExplicit(Co)Products and PreservesExplicit(Co)Products (although that is of course out of the scope of this PR)? LGTM!

Well, this HasExplicitFiniteCoproducts applies only to CompHausLike, i.e. categories of topological spaces which are full subcategories of CompHaus. It just means that the category is closed under taking disjoint unions of topological spaces. This could of course be generalized to other concrete categories.

jcommelin
jcommelin reviewed Sep 3, 2024
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Thanks 🎉

bors merge

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Sep 3, 2024
mathlib-bors bot pushed a commit that referenced this pull request Sep 3, 2024
@dagurtomas @callesonne
feat(Topology/CompHaus): sigma-comparison map (#15525)
79c4b69 
This PR defines the map `CompHausLike.sigmaComparison` associated to a presheaf `X` on
`CompHausLike P`, and a finite family `S₁,...,Sₙ` of spaces in `CompHausLike P`, where `P` is
stable under taking finite disjoint unions.

The map `sigmaComparison` is the canonical map `X(S₁ ⊔ ... ⊔ Sₙ) ⟶ X(S₁) × ... × X(Sₙ)` induced by
the inclusion maps `Sᵢ ⟶ S₁ ⊔ ... ⊔ Sₙ`, and it is an isomorphism when `X` preserves finite
products.



Co-authored-by: Calle Sönne <calle.sonne@gmail.com>
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mathlib-bors bot commented Sep 3, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(Topology/CompHaus): sigma-comparison map [Merged by Bors] - feat(Topology/CompHaus): sigma-comparison map Sep 3, 2024
@mathlib-bors mathlib-bors bot closed this Sep 3, 2024
@mathlib-bors mathlib-bors bot deleted the dagur/SigmaComparison branch September 3, 2024 10:09
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@dagurtomas @callesonne @bjoernkjoshanssen
feat(Topology/CompHaus): sigma-comparison map (#15525)
1323d88 
This PR defines the map `CompHausLike.sigmaComparison` associated to a presheaf `X` on
`CompHausLike P`, and a finite family `S₁,...,Sₙ` of spaces in `CompHausLike P`, where `P` is
stable under taking finite disjoint unions.

The map `sigmaComparison` is the canonical map `X(S₁ ⊔ ... ⊔ Sₙ) ⟶ X(S₁) × ... × X(Sₙ)` induced by
the inclusion maps `Sᵢ ⟶ S₁ ⊔ ... ⊔ Sₙ`, and it is an isomorphism when `X` preserves finite
products.



Co-authored-by: Calle Sönne <calle.sonne@gmail.com>
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@dagurtomas @callesonne @bjoernkjoshanssen
feat(Topology/CompHaus): sigma-comparison map (#15525)
a8992d8 
This PR defines the map `CompHausLike.sigmaComparison` associated to a presheaf `X` on
`CompHausLike P`, and a finite family `S₁,...,Sₙ` of spaces in `CompHausLike P`, where `P` is
stable under taking finite disjoint unions.

The map `sigmaComparison` is the canonical map `X(S₁ ⊔ ... ⊔ Sₙ) ⟶ X(S₁) × ... × X(Sₙ)` induced by
the inclusion maps `Sᵢ ⟶ S₁ ⊔ ... ⊔ Sₙ`, and it is an isomorphism when `X` preserves finite
products.



Co-authored-by: Calle Sönne <calle.sonne@gmail.com>
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 12, 2024
@dagurtomas @callesonne @bjoernkjoshanssen
feat(Topology/CompHaus): sigma-comparison map (#15525)
1db1bea 
This PR defines the map `CompHausLike.sigmaComparison` associated to a presheaf `X` on
`CompHausLike P`, and a finite family `S₁,...,Sₙ` of spaces in `CompHausLike P`, where `P` is
stable under taking finite disjoint unions.

The map `sigmaComparison` is the canonical map `X(S₁ ⊔ ... ⊔ Sₙ) ⟶ X(S₁) × ... × X(Sₙ)` induced by
the inclusion maps `Sᵢ ⟶ S₁ ⊔ ... ⊔ Sₙ`, and it is an isomorphism when `X` preserves finite
products.



Co-authored-by: Calle Sönne <calle.sonne@gmail.com>
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