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What are some examples of AB4* categories? In particular, for a thesis I am writing I need to know if cochain-complexes form an AB4* category

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    $\begingroup$ You posted the first half of this question yesterday - reposting so soon is not acceptable behavior here at MSE. I'd recommend editing this question down to the final bit - "What are some examples of AB4* catergories" and "do cochain-complexes form an AB4* category?" $\endgroup$
    – KReiser
    Commented Jun 2, 2022 at 13:26
  • $\begingroup$ Cochain complexes of … what? Modules? Sheaves of abelian groups? Please be precise! $\endgroup$
    – Zhen Lin
    Commented Jun 2, 2022 at 14:19
  • $\begingroup$ @ZhenLin are there examples of abelian categories $A$ where with all products where the axiom is not satisified for $\mathrm{Ch}(A)$? Or are you worried strictly about completeness? $\endgroup$
    – Stefan Dawydiak
    Commented Jun 2, 2022 at 14:33
  • $\begingroup$ @ZhenLin Modules $\endgroup$
    – Matteo Casarosa
    Commented Jun 2, 2022 at 14:44
  • $\begingroup$ @StefanDawydiak Completeness does not imply AB4*. Sheaves, for example. $\endgroup$
    – Zhen Lin
    Commented Jun 2, 2022 at 14:51

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