On Mon, 7 Feb 2005, Patrik Eklund wrote:
- The Kleisli category of the term monad coincides with its Eilenberg-Moore category and is isomorphic to the category of $\Omega$-algebras. (Is this really true?)
No, this is not true: if $\Omega$ consists of two constant sybmols, the term monad is TX = X+1+1 and the Klesli category does not have a terminal object whereas the Eilenberg-Moore category does. The latter part of the statement is true, see e.g. MacLane. An additional example: Recently, the Eilenberg-Moore category of the infinite-term monad was described as the category of complete Elgot algebras. See J. Adamek, S. Milius and J. Velebil: On Iterative Algebras and Elgot Algebras (submitted) http://www.iti.cs.tu-bs.de/~milius Best, Jiri Adamek