If has finite colimits and a monad preserves reflexive coequalizers, its Eilenberg-Moore category has finite colimits. The forgetful functor creates reflexive coequalizers preserved by . The coproduct presentation for monad algebras yields binary coproducts, and is initial. Any pair can then be replaced by the reflexive pair , with identical coequalizers. Finite coproducts and coequalizers give all finite colimits.
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