feat(CategoryTheory/SmallObject/Iteration): existence of objects (limit case)#19264
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feat(CategoryTheory/SmallObject/Iteration): existence of objects (limit case)#19264
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…iterations of functors in two cases
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
PR summary eeb11676ecImport changes exceeding 2%
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | 429 | 448 | +19 (+4.43%) |
| Mathlib.CategoryTheory.SmallObject.Iteration.Basic | 427 | 440 | +13 (+3.04%) |
| Mathlib.CategoryTheory.SmallObject.Iteration.UniqueHom | 428 | 441 | +13 (+3.04%) |
Import changes for all files
| Files | Import difference |
|---|---|
4 filesMathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone Mathlib.CategoryTheory.SmallObject.Iteration.UniqueHom Mathlib.CategoryTheory.SmallObject.Iteration.Basic |
13 |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty |
19 |
Declarations diff
+ HasIterationOfShape
+ functor
+ hasColimitOfShape_of_isSuccLimit
+ instance [WellFoundedLT J] [HasIterationOfShape C J] (j : J) : Nonempty (Iteration ε j) := by
+ iso_hom_comp_iso_hom
+ map
+ map_comp
+ map_id
+ mkOfLimit
+ restrictionLTFunctorIso
+ restrictionLTFunctorIso_inv_app_map
+ truncFunctor_map_iso_hom
+ trunc_refl
+ trunc_trunc
- iso_trans
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.
Increase in tech debt: (relative, absolute) = (2.00, 0.00)
| Current number | Change | Type |
|---|---|---|
| 1516 | 2 | erw |
Current commit eeb11676ec
Reference commit 5f24fc48e5
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).
joelriou
commented
Dec 20, 2024
This was referenced Dec 20, 2024
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Closed as there is a better version in #20256 |
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Feb 3, 2025
…ns (#20256) The ongoing definition of the iteration of a natural transformation `ε : 𝟭 C ⟶ F` (with `F : C ⥤ C`) is generalized to "successor structures" (which shall become a mathlibism), i.e. in a category `D`, this consists of a zeroth object `X₀`, a successor application `succ : D → D` and, for all `X : D`, a map `toSucc X : X → succ X` (which does not have to be natural: it is not always so in some applications). For such a `Φ : SuccStruct D`, if `J` is a well-ordered type, we define the `J`-th iteration of `Φ`. (In the case `J := ℕ`, this is the colimit of `succ (succ (succ (succ ... X₀)))`.) The iteration of a functor is a particular case of this constructor with `D := C ⥤ C`. As `toSucc` does not have to be natural in `X`, the caveat is that the proofs make extensive use of equalities of objects in `C` and `Arrow C`, while my previous construction used comparison isomorphisms. Nevertheless, the proofs look much more clean now. One of the reasons is that in the inductive construction (file `Iteration.Nonempty`), in the terms of data, we only need to provide a functor, and then all the fields are in `Prop`. (In the downstream API, we shall obviously use isomorphisms instead of equalities...) This PR supersedes #19264. The results are used in #20245 in order to get functorial factorizations in the small object argument. After refactoring my code, I found that this approach had already been used in 2018 by Reid Barton in his pioneering formalization work in Lean 3 towards the model category structure on topological spaces. Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
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Given a functor
Φ : C ⥤ Cand a natural transformationε : 𝟭 C ⟶ Φ, we show that it is possible to iterateεto the powerj : Jfor any well ordered setJ, provided suitable colimits exists inC.See #20256 for a refactored approach.