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3
votes
Algebras for probability monad
The algebras for this monad can be described in essentially the same way: they are sets in which it makes sense to to take "convex combinations" of countably many elements. More precisely, an algebra …
6
votes
Coequalizers in an Eilenberg-Moore category
This question is addressed by Linton [1969, Coequalizers in categories of algebras]. The first step is to notice that, in the presence of binary coproducts, coequalisers exist if and only if reflexive …
6
votes
Further relation between monads and theories
It is well-known that the theories whose category of models are monadic over $\mathbf{Set}$ are necessarily algebraic (possibly infinitary), and conversely every (possibly infinitary) algebraic theory …
20
votes
Accepted
Is there a monad on Set whose algebras are Tychonoff spaces?
No. In fact any full subcategory of $\mathbf{Top}$ that contains all the discrete spaces cannot be monadic over $\mathbf{Set}$ unless it contains only discrete spaces. Indeed, for any such subcategory …