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Timeline for Completion of a category

Current License: CC BY-SA 3.0

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Sep 16, 2013 at 17:43 comment added Michal R. Przybylek @MichalR.Przybylek, the answer is no, and $\cdot \longrightarrow \cdot \stackrel{\longrightarrow}{\longrightarrow} \cdot$ is a counterexample.
Sep 14, 2013 at 8:08 history edited Michal R. Przybylek CC BY-SA 3.0
some minor corrections
Sep 13, 2013 at 20:37 comment added Michal R. Przybylek @ToddTrimble, is there any chance that in our case the category of algebras for the associated idempotent monad coincides with the category of coalgebras for the associated idempotent comonad?
Sep 13, 2013 at 20:11 comment added Michal R. Przybylek @ToddTrimble, of course no! I've learnt much from your answer, and still like it very much. Additionally, in a sense, it answers my question, as it describes a categorification of Dedekind-MacNeille completion.
Sep 13, 2013 at 17:15 comment added Benjamin Steinberg Maybe it is better to keep with a proviso as to where it goes wrong?
Sep 13, 2013 at 17:12 comment added Todd Trimble Should I delete my answer? That would be fine, but I think it has to be "unaccepted" first.
Sep 13, 2013 at 16:39 history answered Michal R. Przybylek CC BY-SA 3.0