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- W4298102575 abstract "Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other triangulated adjunction realizing this monad is 'essentially monadic', i.e. becomes monadic after performing the two evident necessary operations of taking the Verdier quotient by the kernel of the right adjoint and idempotent completion. In this sense, the monad itself is 'intrinsically monadic'. It follows that for any highly structured ring spectrum, its category of homotopy (a.k.a. naive) modules is triangulated if and only if it is equivalent to its category of highly structured (a.k.a. strict) modules." @default.
- W4298102575 created "2022-10-01" @default.
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- W4298102575 date "2016-10-26" @default.
- W4298102575 modified "2023-10-18" @default.
- W4298102575 title "A note on triangulated monads and categories of module spectra" @default.
- W4298102575 doi "https://doi.org/10.48550/arxiv.1610.08387" @default.
- W4298102575 hasPublicationYear "2016" @default.
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