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feat(CategoryTheory): Define subobject classifier #21281

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This creates the folder CategoryTheory/Topos and the file CategoryTheory/Topos/Classifier.lean. The proposed code includes the definition of what it means to be a subobject classifier in a category C with a terminal object, and relevant basic results about such a category. This is done in the "internal" sense, for the purpose of eventually defining what it means for a category to be a topos utilizing this definition; see also #21269.


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@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Jan 31, 2025
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github-actions bot commented Jan 31, 2025

PR summary fc487e3a9f

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.CategoryTheory.Topos.Classifier (new file) 602

Declarations diff

+ Classifier
+ HasClassifier
+ comm
+ isPullback_χ
+ isRegularMonoCategory
+ reflectsIsomorphisms
+ reflectsIsomorphismsOp
+ truth
+ truthIsRegularMono
+ unique
+ Ω
+ χ

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.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-category-theory Category theory label Jan 31, 2025
@CharredLee
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CharredLee commented Jan 31, 2025

Note that the reason for not putting this in the folder CategoryTheory/Subobject is precisely because it uses the "internal" definition. A future extension of this content will be to define CategoryTheory/Subobject/Classifier.lean and show that the "external" definition of a subobject classifier (that the Sub functor is representable) is equivalent.

@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes label Jan 31, 2025
CharredLee and others added 4 commits January 31, 2025 09:14
rename `Classifier.pullback` to `Classifier.isPullback`

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
@CharredLee CharredLee removed the awaiting-author A reviewer has asked the author a question or requested changes label Feb 3, 2025
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes label Feb 3, 2025
@CharredLee CharredLee removed the awaiting-author A reviewer has asked the author a question or requested changes label Feb 3, 2025
@CharredLee CharredLee requested a review from joelriou February 3, 2025 17:02
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes label Feb 4, 2025
@CharredLee CharredLee removed the awaiting-author A reviewer has asked the author a question or requested changes label Feb 4, 2025
@CharredLee CharredLee requested a review from joelriou February 4, 2025 13:29
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes label Feb 16, 2025
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I'm happy with the maths here, just style and naming questions now. We briefly discussed how the limit assumptions should be set up, I think we agreed that the one here is sensible for now?

@CharredLee CharredLee removed the awaiting-author A reviewer has asked the author a question or requested changes label Feb 21, 2025
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