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- W2912349790 abstract "Abstract Let $${mathbb {A}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>A</mml:mi> </mml:math> be a 2-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism p exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the two-dimensional cokernel diagram of p is up to isomorphism the same as the semantic factorization of p , either one existing if the other does. The result can be seen as a counterpart account to the celebrated Bénabou–Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of p trivially hold whenever p has a left adjoint and, hence, in this case, we find monadicity to be a two-dimensional exact condition on p , namely, to be an effective faithful morphism of the 2-category $${mathbb {A}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>A</mml:mi> </mml:math> ." @default.
- W2912349790 created "2019-02-21" @default.
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- W2912349790 date "2022-11-15" @default.
- W2912349790 modified "2023-09-26" @default.
- W2912349790 title "Semantic Factorization and Descent" @default.
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- W2912349790 doi "https://doi.org/10.1007/s10485-022-09694-w" @default.
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