[Merged by Bors] - feat(CategoryTheory): κ-filtered categories#20005
Closed
[Merged by Bors] - feat(CategoryTheory): κ-filtered categories#20005
κ-filtered categories#20005Conversation
… category-theory-arrow-cardinal
… category-theory-arrow-cardinal
3 tasks
PR summary 1936c67d86Import changes exceeding 2%
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.SetTheory.Cardinal.HasCardinalLT | 660 | 782 | +122 (+18.48%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.CategoryTheory.Comma.CardinalArrow Mathlib.SetTheory.Cardinal.HasCardinalLT |
122 |
Mathlib.CategoryTheory.Presentable.IsCardinalFiltered (new file) |
864 |
Declarations diff
+ IsCardinalFiltered
+ WalkingParallelFamily.arrowEquiv
+ cocone
+ coeq
+ coeqHom
+ coeq_condition
+ fact_isRegular_aleph0
+ hasCardinalLT_arrow_walkingParallelFamily
+ hasCardinalLT_option_iff
+ instance [Small.{w'} C] [LocallySmall.{w} C] :
+ isCardinalFiltered_aleph0_iff
+ isCardinalFiltered_preorder
+ isFiltered_of_isCardinalDirected
+ max
+ of_le
+ toCoeq
+ toMax
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
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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…nto category-theory-is-cardinal-filtered
11 tasks
This was referenced Dec 26, 2024
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
…into category-theory-is-cardinal-filtered
…into category-theory-is-cardinal-filtered
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Jan 23, 2025
If `κ` is a regular cardinal, we introduce the notion of `κ`-filtered category `J`: it means that any functor `A ⥤ J` from a small category such that `Arrow A` is of cardinality `< κ` admits a cocone. This generalizes the notion of filtered category. Indeed, we obtain the equivalence `IsCardinalFiltered J ℵ₀ ↔ IsFiltered J`. The API is mostly parallel to that of filtered categories. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
κ-filtered categoriesκ-filtered categories
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If
κis a regular cardinal, we introduce the notion ofκ-filtered categoryJ: it means that any functorA ⥤ Jfrom a small category such thatArrow Ais of cardinality< κadmits a cocone. This generalizes the notion of filtered category. Indeed, we obtain the equivalenceIsCardinalFiltered J ℵ₀ ↔ IsFiltered J. The API is mostly parallel to that of filtered categories.Arrow Ais finite iffAis a finite category #19945