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nLab > Latest Changes: category of chain complexes

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2012
    • (edited Sep 2nd 2012)

    I have polished category of chain complexes a little more and started a section (but unfinished) with discussion of that and how Ch •(𝒜)Ch_\bullet(\mathcal{A}) is itself again an abelian category

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 6th 2015

    There seems to be some confusion (including my confusion!) as to the usual notation for ‘bounded above’ chain complexes, etc., on the page category of chain complexes , when I compare the notation with Weibel (and several others). Weibel (page 3) uses Ch −Ch_{-} for bounded above , Ch +Ch_{+} for bounded below.

    • CommentRowNumber3.
    • CommentAuthorsamwinnick
    • CommentTimeOct 11th 2022
    For the two propositions at the bottom, concerning the category $\mathrm{Ch}(A)$ of chain complexes in an additive category $A$ being monoidal or closed monoidal, I think that we need to require $A$ to be monoidal resp. closed monoidal beyond just being additive. This is achieved if $A=R\mathrm{-mod}$ where $R$ is a monoid in some monoidal category, since objects of $A$ get a monoidal product $\otimes_R$.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2023
    • (edited Apr 18th 2023)

    added the statement (here) that chain complexes in a Grothendieck category are themselves Grothendieck abelian and hence locally presentable

    diff, v19, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2023
    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeDec 16th 2023

    Missing (R Mod)

    diff, v22, current

1 to 6 of 6

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