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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 …
Zhen Lin's user avatar
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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 …
Zhen Lin's user avatar
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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 …
Zhen Lin's user avatar
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20 votes
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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 …
Zhen Lin's user avatar
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