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nLab > Latest Changes: cotensor product

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2016

    I have added to cotensor product a section, here, with some basics on cotensor products of comodules over commutative Hopf algebroids. The same stuff I have added also in the respective section at commutative Hopf algebroid

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 21st 2019
    • Samuel Eilenberg, John. C Moore, Homology and fibrations. I. Coalgebras, cotensor product and its derived functors, Comment. Math. Helv. 40 (1966) 199–236 MR203730 doi

    diff, v8, current

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeNov 21st 2019

    Few words more about induced comodules, along with a reference on Doi on homological properties of cotensor products. Doi unfortunately has all discussion for coalgebras over fields, what is insufficient for many modern applications with coalgebras over commutative rings where more nontrivial non-exactness phenomena have to be observed (or even worse for cotensor products over corings, that is coalgebras in the nonsymmetric categories of bimodules).

    diff, v8, current

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 21st 2019

    Added references of Positelski on semi-infinite homological algebra and

    • T. Brzeziński, R. Wisbauer, Corings and comodules, London Math. Soc. Lec. Note Series 309, Cambridge 2003.

    where (in both refs) the cotensor products are worked for coalgebras over commutative rings or in the categories of bimodules.

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeNov 22nd 2019

    Maybe we should add a hatnote that “cotensor” is also used for powers in an enriched category, and for the multiplicative disjunction in a linearly distributive category?

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 22nd 2019

    I agree that’s a good idea, Mike.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeNov 22nd 2019

    Added hatnote.

    diff, v9, current

1 to 7 of 7

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