Timeline for Contramodule as direct limit of its finitely generated subcontramodules
Current License: CC BY-SA 4.0
5 events
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| Feb 23, 2021 at 14:07 | comment | added | Leonid Positselski | Concerning the infinitary Morita theory and the related result on how to make the forgetful functor fully faithful by replacing a topological ring $R$ by a bigger topological ring $S$, the related references are "The tilting-cotilting correspondence", arxiv.org/abs/1710.02230 (IMRN 2021, by Jan Stovicek and me), Sections 6.4 and 7.3 (see also "Abelian right perpendicular subcategories in module categories", arxiv.org/abs/1705.04960 , Theorem 6.4.). | |
| Feb 23, 2021 at 13:42 | comment | added | Leonid Positselski | For an overview and discussion, see the same preprint "Contramodules", arxiv.org/abs/1503.00991 , Section 3.8. | |
| Feb 23, 2021 at 13:41 | comment | added | Leonid Positselski | For a much more advanced version, in the case of (conilpotent) coalgebras over a field, see the paper "Smooth duality and co-contra correspondence", arxiv.org/abs/1609.04597 (J. Lie Theory 30, 2020), Theorem 2.1. In the context of topological rings, the reference is "Abelian right perpendicular subcategories in module categories", arxiv.org/abs/1705.04960 , Theorem 3.1, or better yet, "Flat ring epimorphisms of countable type", arxiv.org/abs/1808.00937 (Glasgow Math. J. 62, 2020), Theorem 6.2 or Corollary 6.7. For an overview and discussion... | |
| Feb 23, 2021 at 13:30 | comment | added | Leonid Positselski | I have been asked privately to elaborate on examples or conditions when the forgetful functor $R{-}\mathbf{contra}\to R{-}\mathbf{mod}$ or $C{-}\mathbf{contra}\to C^*{-}\mathbf{mod}$ is fully faithful. The simplest result of this kind goes back to Theorem B.1.1(1) in "Weakly curved A-infinity algebras over a topological local ring", arxiv.org/abs/1202.2697 (Memoires SMF 159, 2018); see Section 1.6 in the preprint "Contramodules" arxiv.org/abs/1503.00991 cited in the question for a discussion. | |
| Feb 18, 2021 at 18:15 | history | answered | Leonid Positselski | CC BY-SA 4.0 |