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[Merged by Bors] - feat(CategoryTheory): Arrow A is finite iff A is a finite category#19945

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[Merged by Bors] - feat(CategoryTheory): Arrow A is finite iff A is a finite category#19945
joelriou wants to merge 16 commits intomasterfrom
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@joelriou joelriou commented Dec 13, 2024 •
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@joelriou joelriou added the t-category-theory Category theory label Dec 13, 2024
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Update Mathlib/CategoryTheory/Comma/CardinalArrow.lean
15b40c4 
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
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feat(CategoryTheory): the equivalence of categories induced by a bije…
1264ce9 
…ction (#20881)

When `f : T → D` is a map and `D` is a category, then `InducedCategory D f` is a category with objects `T` with a fully faithful functor to `D`. In this PR, we show that in the case of a bijection `T ≃ D`, the induced category is equivalent to `D`.

The code would be nicer (see #19945) if the type of morphisms in the induced category was defined as a 1-field structure. This would be a very welcomed refactor.
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mathlib4-dependent-issues-bot commented Jan 21, 2025

This PR/issue depends on:

@leanprover-community-bot-assistant leanprover-community-bot-assistant added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jan 21, 2025
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PR summary 9500f6759d

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.CategoryTheory.Comma.CardinalArrow (new file) 708

Declarations diff

+ Arrow.discreteEquiv
+ Arrow.equivSigma
+ Arrow.finite
+ Arrow.finite_iff
+ Arrow.opEquiv
+ Arrow.shrinkEquiv
+ Arrow.shrinkHomsEquiv
+ ext
+ hasCardinalLT_arrow_discrete_iff
+ hasCardinalLT_arrow_op_iff
+ hasCardinalLT_arrow_shrinkHoms_iff
+ hasCardinalLT_arrow_shrink_iff
+ hasCardinalLT_of_hasCardinalLT_arrow
+ locallySmall_of_small_arrow
+ small_of_small_arrow

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).

@joelriou joelriou removed the awaiting-author A reviewer has asked the author a question or requested changes. label Jan 21, 2025
@leanprover-community-bot-assistant leanprover-community-bot-assistant removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jan 21, 2025
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Thanks!
bors r+

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Jan 21, 2025
mathlib-bors bot pushed a commit that referenced this pull request Jan 21, 2025
@joelriou
feat(CategoryTheory): Arrow A is finite iff A is a finite category (
9db6595 
#19945)

We obtain various results about the cardinality of `Arrow`.



Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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mathlib-bors bot commented Jan 21, 2025

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(CategoryTheory): Arrow A is finite iff A is a finite category [Merged by Bors] - feat(CategoryTheory): Arrow A is finite iff A is a finite category Jan 21, 2025
@mathlib-bors mathlib-bors bot closed this Jan 21, 2025
@mathlib-bors mathlib-bors bot deleted the category-theory-arrow-cardinal branch January 21, 2025 18:35
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