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9 votes
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When do functors induce monadic adjunctions to presheaf categories

I will try to give an answer to your first question. The functor $\Delta_F$ verifies automatically nearly all the conditions of the monadicity theorem: it is a right adjoint; it is a left adjoint w …
Ricardo Andrade's user avatar
9 votes
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When do reflexive coequalizers preserve weak equivalences?

Moreover, in the specific case of algebras for monads, it may be a good idea to think about simplicial objects and geometric realizations instead of reflexive coequalizers. …
Ricardo Andrade's user avatar