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Timeline for Seeing modules as ring extensions

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Apr 20, 2017 at 6:19 answer added Tim Porter timeline score: 2
Apr 20, 2017 at 6:00 comment added user44191 @მამუკაჯიბლაძე I don't think it's quite a duplicate, although somewhat related. S Carnahan's answer seems to partially match my idea, if we restrict to $k$-categories; magmas would be acting in exactly the same way as not-necessarily-commutative algebras as above.
Apr 20, 2017 at 5:44 comment added მამუკა ჯიბლაძე Closely related (possibly duplicate): Do non-associative objects have a natural notion of representation?
Apr 20, 2017 at 4:56 comment added ಠ_ಠ There's some explanation of Beck's definition on the nLab as well.
Apr 20, 2017 at 4:49 history edited user44191 CC BY-SA 3.0
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Apr 20, 2017 at 4:32 history edited user44191 CC BY-SA 3.0
Partial answer to question 1
Apr 20, 2017 at 3:29 comment added darij grinberg This looks to me like how Beck defines $X$-modules for $X$ being an object in a category. See Jonathan Mock Beck, Triples, algebras and cohomology, Reprints in Theory and Applications of Categories, No. 2 (2003) pp 1-59, as cited in §2 of Lars Hesselholt, The big de Rham-Witt complex, arXiv:1006.3125v3. (Beware: I have only a passing familiarity with the latter and none at all with the former.)
Apr 20, 2017 at 3:22 history asked user44191 CC BY-SA 3.0