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• 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 $Ch_\bullet(\mathcal{A})$ 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 $Ch_{-}$ for bounded above , $Ch_{+}$ 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 $\otimes_R$.