= Finite colimits of monad algebras from reflexive coequalizers
If $\mathcal C$ has finite <colimits> and a <monad> $T$ preserves <reflexive coequalizers>, its <Eilenberg-Moore category> has finite colimits. The forgetful <functor> creates reflexive coequalizers preserved by $T$. The <coproduct presentation for monad algebras> yields binary coproducts, and $F0$ is initial. Any pair $a,b:X\rightrightarrows Y$ can then be replaced by the <reflexive pair> $[a,1],[b,1]:X+Y\rightrightarrows Y$, with identical coequalizers. Finite coproducts and coequalizers give all finite colimits.
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