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nLab > Latest Changes: question at [[CommCoalg]]

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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 23rd 2009

    I put a question at CommCoalg for those knowledgeable about accessible categories: is this category locally presentable?

    • CommentRowNumber2.
    • CommentAuthorGavinWraith
    • CommentTimeNov 27th 2009
    You bet - for comm. coalgebras over a field at any rate. Every object is a
    filtered colimit, union in fact, of finite-dimensional ones, and Hom-ing out
    of a finite-dimensional coalgebra preserves filtered colimits. Or did I misunderstand?
    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 29th 2009

    Thanks, Gavin. It's the second statement I'm having trouble seeing clearly. Is it obvious, or a standard result?

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