Timeline for Reference request: Algebras over monoid objects in a monoidal category [duplicate]

Current License: CC BY-SA 4.0

11 events

when toggle format	what		by	license	comment
Dec 3 at 20:48	history	closed	Peter LeFanu Lumsdaine Daniele Tampieri gmvh CommunityBot		Duplicate of The change-of-monoid adjunction between categories of modules induced by a morphism of monoids
Dec 3 at 20:45	vote	accept	ari rosenfield
Dec 3 at 10:21	history	became hot network question
Dec 3 at 9:24	comment	added	Vladimir Dotsenko		It is certainly mentioned matter-of-factly as completely well known in "Coequalizers in categories of algebras" of Linton (link.springer.com/chapter/10.1007/BFb0083082). One may argue that this is already in "Functorial semantics of algebraic theories" of Lawvere (pnas.org/doi/abs/10.1073/pnas.50.5.869), though of course there it is mentioned (as obvious) for equational algebraic theories only.
S Dec 3 at 9:02	history	suggested	J. W. Tanner		added ref tag
Dec 3 at 8:29	answer	added	varkor		timeline score: 6
Dec 3 at 8:13	review	Close votes
Dec 3 at 20:57
Dec 3 at 7:57	comment	added	Peter LeFanu Lumsdaine		This was asked last year under different terminology: The change-of-monoid adjunction between categories of modules induced by a morphism of monoids. (Though if you just want the monad case, that’s a bit more specific and might be out there somewhere else.)
Dec 3 at 4:45	comment	added	Qiaochu Yuan		That phrasing is a little ambiguous; it seems clearer to say that pullback along $\phi$ defines a functor from $T$-algebras to $S$-algebras, etc. Even in familiar examples there may be more than one candidate for $\phi$, e.g. there are two homomorphisms from the monoid monad to the ring monad, corresponding to addition and multiplication.
Dec 3 at 4:39	review	Suggested edits
S Dec 3 at 9:02
Dec 3 at 1:46	history	asked	ari rosenfield	CC BY-SA 4.0