[Merged by Bors] - feat(Algebra/Category/ModuleCat): composition of restriction of scalar functors#6915
Closed
[Merged by Bors] - feat(Algebra/Category/ModuleCat): composition of restriction of scalar functors#6915
Conversation
1 task
bors bot
pushed a commit
that referenced
this pull request
Sep 8, 2023
…r functors (#6915) This PR studies the behaviour of restriction of scalars functors with respect to composition.
|
Pull request successfully merged into master. Build succeeded! The publicly hosted instance of bors-ng is deprecated and will go away soon. If you want to self-host your own instance, instructions are here. If you want to switch to GitHub's built-in merge queue, visit their help page. |
Julian
added a commit
that referenced
this pull request
Sep 11, 2023
* fix-lint: (463 commits) chore: lint-style.py was calling str.replace incorrectly chore: module doc for #find_home, #minimize_imports, import early (#7095) chore: reduce imports to Data.Rat.Cast.CharZero (#7091) chore: cleanup imports of Data/Rat/Cast/Defs (#7092) chore: linarith only needs ring1 (#7090) refactor(Data/Int/Bitwise): use `<<<` and `>>>` notation (#6789) chore: delete redundant commented-out positivity test (#7085) chore: fix docstrings, names and aligns about paracompacity of emetric spaces (#7064) feat(Data/Finsupp): add notation (#6367) refactor: re-home some meta code (#6921) fix: don't use `False` as a bool, use `false` (#7059) chore: fix reference to `compactCovering` in docstring (#7065) fix: fix link in docstring of IsWellFounded (#7063) chore: tidy various files (#7041) feat: roots in an algebra (#6740) chore: revert ProofWidgets bump in #7044 and #7056 (#7069) feat: super factorial (#6768) feat(LinearAlgebra/Matrix/Trace): add Matrix.trace_diagonal (#7061) chore: complete ProofWidgets bump (#7056) feat: More `Finset.sup'` lemmas (#7021) feat: self_lt_pow (#7058) chore: move some files to `MeasureTheory/MeasurableSpace/` (#7045) chore(RingTheory/Nilpotent): untwine two universes (#7057) feat: von Neumann Mean Ergodic Theorem (#6053) feat: (sSup, Iic) and (Ici, sInf) are Galois connections (#6951) feat: derivative along a vector (#7038) feat: check for some common git problems in CI (#7043) chore: bump ProofWidgets (#7044) feat(Topology/Algebra): add `DiscreteTopology Mˣ` (#7028) chore: simplify `by rfl` (#7039) chore: tidy various files (#7035) refactor(LinearAlgebra/CliffordAlgebra/Conjugation): expose implementation details of 'reverse' (#6783) feat: add `DiscreteTopology.of_continuous_injective` (#7029) feat: restore the module docstring code snippet (#7030) feat: flesh out the API for `realPart` and `imaginaryPart` (#7023) chore: missing simps lemmas for `Multiplicative` defs (#7016) feat: characterize isLittleO on principal filters (#7008) doc: cleanup documentation on Basis.constr (#7007) feat: cleanup API around differentiable functions (#7004) feat: add Nat.digits_append_digits (#6999) feat: definition of the homology of a short complex (#6994) chore: implement porting notes about Polish spaces (#6991) feat(Algebra/Category/ModuleCat): composition of restriction of scalar functors (#6915) feat: compute the integral of sqrt (1 - x ^ 2) (#6905) chore(*/TensorProduct): missing functorial lemmas (#6781) feat: a functor from a small category to a filtered category factors through a small filtered category (#6212) feat: expand API on locally integrable functions (#7006) chore: split Tactic.NormNum.Basic (#7002) feat: a few lemmas on continuous functions (#7005) feat: ZMod.castHom_self (#7013) ...
kodyvajjha
pushed a commit
that referenced
this pull request
Sep 22, 2023
…r functors (#6915) This PR studies the behaviour of restriction of scalars functors with respect to composition.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This PR studies the behaviour of restriction of scalars functors with respect to composition.
(This PR also relates semilinear maps and linear maps to a restriction of scalars. It also fixes a namespace problem: as
ModuleCatis in the root namespace, there is no reason to introduceCategoryTheory.ModuleCatin theChangeOfRingsfile. I hope the diff is still readable...)In order to construct limits in the category of presheaves of modules over a presheaf of rings
R, it is important to study the properties of the restriction of scalars functors, and how they behave with respect to composition (in more abstract terms, there is a prefibered category of modules over the (opposite) category of rings, and the restriction of scalars functors are the direct image functors, and we want to show it is a fibered category, i.e. direct image functors compose well).Actually, the restriction of scalars functors behave very well, as the composition of two restriction of scalars functors is defeq to the restriction of scalars of the composition. However, if we try to apply this to the restriction of scalars for ring morphisms
R.map f, thenR.map (f ≫ g) = R.map f ≫ R.map gis no longer a defeq, which is the reason why I have introducedrestrictScalarsComp'which takes as an input an equalitygf = g.comp f.