[Merged by Bors] - feat(CategoryTheory): Grothendieck abelian categories have enough injectives#20079
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[Merged by Bors] - feat(CategoryTheory): Grothendieck abelian categories have enough injectives#20079
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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>
…ctives.lean Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
…' into grothendieck-abelian-enough-injectives
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This is great, thank you so much for working on this!
Mathlib/CategoryTheory/Abelian/GrothendieckCategory/EnoughInjectives.lean
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bors d+ |
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✌️ joelriou can now approve this pull request. To approve and merge a pull request, simply reply with |
…ctives.lean Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
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Thanks for the reviews! bors merge |
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…ectives (#20079) We formalize the theorem by Grothendieck that abelian categories which have exact filtering colimits and a generator have enough injectives (*Sur quelques points d'algèbre homologique*, Tôhoku Mathematical Journal 9, 1957). Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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* origin/master: chore(*): add `@[fun_prop]` (#22183) chore(RingTheory): generalize universes for `isUnramified_iff_map_eq` (#22185) chore(Algebra/GroupPower/IterateHom): move all lemmas earlier (#22132) feat(Probability): ae filter and integrability wrt a composition of kernel and measure (#22074) feat(CategoryTheory): forgetting the group structure on the codomain of left-exact functors (#21973) feat(CategoryTheory): embeddings for opposites of Grothendieck abelian categories (#22182) feat(CategoryTheory): `AsSmall C` is abelian (#22184) feat(CategoryTheory): explicit argument versions of `epi_comp` and `mono_comp` (#22181) feat(Topology/Instances/EReal/Lemmas): add lemmas about limsup and multiplication (#21833) feat: basic structural lemmas about finite crystallographic root pairings. (#21932) Rename `Mem𝓛p` to `MemLp` (#22164) feat(Logic/Equiv): Upgrade arrowProdEquivProdArrow to dependent types (#21518) feat(CategoryTheory): Grothendieck abelian categories have enough injectives (#20079) chore: deprecate Finite.cast_card_eq_mk (#22161) feat(CategoryTheory/Limits/Fubini): relax `HasLimits` hypotheses (#20570) chore(Algebra/Order/Monoid/Unbundled/WithTop): golf, clean up (#22109)
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We formalize the theorem by Grothendieck that abelian categories which have exact filtering colimits and a generator have enough injectives (Sur quelques points d'algèbre homologique, Tôhoku Mathematical Journal 9, 1957).