Dear Emily, You are in luck. Your result is an instance of the following: PROP If C is a category bearing the orthogonal factorisation system (E,M), and T is a monad on C whose underlying functor preserves E-maps, then C^T bears the orthogonal factorisation system (U^-1(E), U^-1(M)). A full proof of which is given as Proposition 20.28 in: Abstract and concrete categories: The joy of cats (Wiley, 1990) Jiri Adamek, Horst Herrlich and George Strecker Maybe there is an older reference than this but I am not aware of such. Richard On 14 April 2012 08:09, Emily Riehl <eriehl@math.harvard.edu> wrote:
I've placed a bet with a colleague that the following result appears in the literature. Please help me win.
Claim: Suppose (E,M) is an orthogonal factorization system (unique lifts) on a symmetric monoidal category and X is a fixed monoid. If tensoring with X preserves maps in the class E, then (E,M) lifts to an orthogonal factorizaiton system on the category of X-modules.
Regards, Emily Riehl
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