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Oct 1, 2022 at 5:58 history edited Martin Sleziak CC BY-SA 4.0
a minor typo
Jul 23, 2021 at 13:37 comment added user319449 Thanks, it'll take time to read. the factorisation system (mono,epi), any "submorphism" of a mono is a mono. May a condition like this on I be hepful to show that M is based under co-base change ? Something like this is true in the examples from model theory I care about. (But not quite like this)
Jul 22, 2021 at 15:32 comment added Tim Campion Here's another special case which may be related to "goodness": Suppose that we work in a category with disjoint coproducts, and suppose that the codomains $j$ of the morphsims $i \to j$ of $I$ are all connected (i.e. $Hom(j,-)$ preserves coproducts). Then $\mathcal M$ is closed under coproducts.
Jul 22, 2021 at 15:26 history answered Tim Campion CC BY-SA 4.0