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    • CommentRowNumber1.
    • CommentAuthorSridharRamesh
    • CommentTimeMar 4th 2010
    In Todd Trimble's article "Three topos theorems in one" on his private area of the nlab, he asks for a published reference for the result that the category of coalgebras for a pullback-preserving comonad on a topos is itself a topos. I'm not sure if he's still interested, but in case he is, Remark 4.2.3 in section A of Sketches of an Elephant points out precisely this fact. (I originally thought I would simply edit the article to provide the reference, but was unable to do so, lacking editing privileges on Todd's private area. Then I thought I'd e-mail Todd to let him know, but couldn't find his e-mail address. So, finally, I settled for posting this on the forum, as presumably the next best thing)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 4th 2010

    as presumably the next best thing

    Or even the best thing! :-)

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 4th 2010
    • (edited Mar 4th 2010)

    Thanks, Sridhar! I should have edited this in already; Mike Shulman told me this some time ago. Sorry to make people duplicate efforts. (I've got to get hold of that Elephant! Does it say who first observed this fact?)

    In case someone wants to reach me, they can do so at But I agree with Urs that writing here is often best.

    [Edit: the article now has the reference.]

    • CommentRowNumber4.
    • CommentAuthorSridharRamesh
    • CommentTimeMar 4th 2010
    Ah, yeah, I thought you might've already found it by now. Alas, it does not say who first made the observation.