TITLE: Reference request: (co)limits in Eilenberg--Moore (V-)categories
QUESTION [7 upvotes]: The following result seems to be well known:

If T is a (V-)monad on a (V-)category C, then the forgetful functor $U^T \colon C^T \to C$ creates

any limits that exist in C, and
any colimits that exist in C and are preserved by T.


But I don't know of a published proof for general V.  Toposes, Triples and Theories proves (1) for V = Set and leaves (2) for the special case of coequalizers as an exercise.  Kelly's book doesn't mention monads at all.  Lack, in Codescent objects and coherence, says that 'of course' (2) is true for V = Cat, but doesn't give a citation, while Blackwell, Kelly & Power, in 2-dimensional monad theory, say that (1) is 'well known' but don't give a reference either.  And so on.
My questions are:

Has a complete proof of this result (assuming it's true as stated) been published?
Has its bicategorical analogue been treated?

REPLY [4 votes]: A result slightly weaker than your point 1. (creation of limits) for general enriched categories can be found in
Eduardo J. Dubuc, Kan extensions in Enriched Category Theory, Lecture Notes in Mathematics, Volume 145, 1970, Chapter II
where a few special cases are proved. Proposition II.4.7, Dubuc proves that powers (also known as cotensors) are created, and Proposition II.4.8 covers conical limits and ends. (The proof of the first proposition is very detailed, while the second is mostly left as an exercise.)
Taken together, these results show that the category of algebras is complete if the base is. I do not know a reference for creation of a general weighted limit (which might exist even if the category doesn't have copowers, products, and ends), nor for the creation of colimits that are preserved by $T$.