[Merged by Bors] - feat(category_theory/closed): Frobenius reciprocity of cartesian closed categories #5624
Conversation
This file contains 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
b-mehta
added
the
awaiting-review
github-actions
bot
added
the
blocked-by-other-PR
github-actions
bot
added
merge-conflict
|
🎉 Great news! Looks like all the dependencies have been resolved: 💡 To add or remove a dependency please update this issue/PR description. Brought to you by Dependent Issues (:robot: ). Happy coding! |
github-actions
bot
removed
the
merge-conflict
b-mehta
commented
Jan 8, 2021
| apply nat_iso.is_iso_of_is_iso_app _, | ||
| intro B, | ||
| dsimp [frobenius_morphism], | ||
| apply_instance, |
There was a problem hiding this comment.
By the way Johan, this is how I knew that the preserves products assumption was enough to make is_iso prod_comparison_nat_trans when you asked the question about that earlier :)
|
✌️ b-mehta can now approve this pull request. To approve and merge a pull request, simply reply with |
b-mehta
commented
Jan 8, 2021
b-mehta
commented
Jan 8, 2021
Co-authored-by: Johan Commelin <johan@commelin.net>
|
bors r+ |
bors bot
pushed a commit
that referenced
this pull request
Jan 8, 2021
…ed categories (#5624) A re-do of #4929. Re-defines the exponential comparison morphism (now as a natural transformation rather than a morphism with a naturality prop), and defines the Frobenius reciprocity morphism for an adjoint. In the case where the functor has a left adjoint, gives a sufficient condition for it to be cartesian closed, and a sufficient condition for a functor whose left adjoint preserves binary products to be cartesian closed (but doesn't show the necessity of this). - [x] depends on: #5623
|
Pull request successfully merged into master. Build succeeded: |
bors
bot
changed the title
Julian
added a commit
that referenced
this pull request
Jan 12, 2021
* origin/master: (751 commits) chore(topology/algebra/infinite_sum): speedup has_sum_sum (#5710) feat(submonoid/basic): subsingleton and nontrivial instances for {add_,}submonoid (#5690) docs(undergrad.yaml): analysis updates (#5675) feat(linear_algebra/multilinear_map): Add `range` and `map` (#5658) feat(measure_theory): each set has a measurable superset of the same measure (#5688) feat(data/set/intervals): add 2 Icc ssubset lemmas (#5617) chore(category_theory/limits): move constructions folder (#5681) fix(linear_algebra/tensor_product): Remove the priorities from the module structure (#5667) chore(category_theory/limits/over): generalise, golf and document over limits (#5674) chore(scripts): update nolints.txt (#5705) feat(measure_theory/pi): `ae_eq` lemmas about intervals in `Π i, α i` (#5633) feat(algebra/splitting_field): Restrict to splitting field (#5562) chore(scripts): update nolints.txt (#5699) feat(analysis/special/functions/trigonometric): complex trig and some even/odd lemmas (#5404) feat(equiv|set|topology): various additions (#5656) chore(measure_theory/set_integral): use weaker assumptions here and there (#5647) feat(field_theory/separable): Remove hypothesis in irreducible.separable (#5687) feat(order/complete_well_founded): characterise well-foundedness for complete lattices (#5575) chore(order/filter): a few more lemmas about `eventually` and set operations (#5686) chore(order/filter/basic): a few `simp` lemmas (#5685) feat(data/equiv/basic, logic/embedding): swap commutes with injective functions (#5636) chore(scripts): update nolints.txt (#5682) feat(algebra/lie/basic): Lie ideal operations are linear spans (#5676) feat(measure_theory/lp_space): add more lemmas about snorm (#5644) chore(data/set/lattice): add a few simp lemmas (#5671) feat(topology/separation, topology/metric_space/basic): add lemmas on discrete subsets of a topological space (#5523) feat(topology/algebra/ordered): prove `tendsto.Icc` for pi-types (#5639) chore(scripts): update nolints.txt (#5673) feat(category_theory/limits): preserving pullbacks (#5668) chore(linear_algebra/alternating): golf a proof (#5666) chore(algebra/group/hom): fix additive version of docstring (#5660) chore(analysis/special_functions/trigonometric): adding `@[pp_nodot]` to complex.log (#5670) feat(data/finset/intervals, data/set/intervals/basic): intersection of finset.Ico, union of intervals for sets and finsets (#5410) feat(algebra/linear_ordered_comm_group_with_zero): Add linear_ordered_comm_monoid_with_zero and an instance for nat (#5645) feat(geometry/manifold/times_cont_mdiff): API for checking `times_cont_mdiff` (#5631) feat(category_theory/closed): Frobenius reciprocity of cartesian closed categories (#5624) feat(measure_theory/measure_space): ae_measurable and measurable are equivalent for complete measures (#5643) refactor(linear_algebra/alternating): Use unapplied maps when possible (#5648) chore(algebra/ordered_monoid): rename lemmas (#5657) feat(measure_theory/borel_space): locally finite measure is sigma finite (#5634) refactor(algebra/module/basic): Clean up all the nat/int semimodule definitions (#5654) feat(topology/algebra): add additive/multiplicative instances (#5662) chore(scripts): update nolints.txt (#5661) feat(measure_theory): some additions (#5653) chore(data/list/basic): tag mmap(') with simp (#5443) feat(category_theory/sites): category of sheaves on the trivial topology (#5651) feat(category_theory/monad): reflector preserves terminal object (#5649) feat(measure_theory/borel_space): a compact set has finite measure (#5628) feat(category_theory/closed): golf definition and proofs (#5623) feat(category_theory/limits): the product comparison natural transformation (#5621) ...
YaelDillies
removed
the
awaiting-review
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
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.
A re-do of #4929.
Re-defines the exponential comparison morphism (now as a natural transformation rather than a morphism with a naturality prop), and defines the Frobenius reciprocity morphism for an adjoint. In the case where the functor has a left adjoint, gives a sufficient condition for it to be cartesian closed, and a sufficient condition for a functor whose left adjoint preserves binary products to be cartesian closed (but doesn't show the necessity of this).