Lemma 5.9. Assuming that:

• $C\underset{G}{\overset{F}{\rightleftarrows }}D$ is an adjunction inducing the monad $𝕋$ on $C$

• for every $𝕋$ algebra $(A,\alpha )$, the pair $FGFA\underset{{𝜀}_{FA}}{\overset{F\alpha }{\rightrightarrows }}FA$ has a coequaliser in $D$