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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 7th 2011
    • (edited Oct 7th 2011)

    I added more to idempotent monad, in particular fixing a mistake that had been on there a long time (on the associated idempotent monad). I had wanted to give an example that addresses Mike’s query box at the bottom, but before going further, I wanted to track down the reference of Joyal-Tierney, or perhaps have someone like Zoran fill in some material on classical descent theory for commutative algebras (he wrote an MO answer about this once) to illustrate the associated idempotent monad.

    Some of this (condition 2 in the proposition in the section on algebras) was written as a preparatory step for a to-be-written nLab article on Day’s reflection theorem for symmetric monoidal closed categories, which came up in email with Harry and Ross Street.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 8th 2011

    Thanks! I fixed a bit of formatting, and changed some appearances of RLR L to MM which it seemed like they wanted to be.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2014
    • (edited Jan 14th 2014)

    I have made more explicit the statement that the Eilenberg-Moore category of an idempotent monad induced by a reflection reproduces the underlying reflective subcategory; at idempotent monad, at reflective subcategory and at Eilenberg-Moore category, pointing also to Borceux vol 2.

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