Proposition 5.8. Assuming that:

• $𝕋$ a monad on $C$

• (i) The forgetful functor $G^{𝕋}:C^{𝕋}\to C$ creates all limits which exist in $C$.
• (ii) If $C$ has colimits of shape $J$, then $G^{𝕋}$ creates colimits of shape $J$ if and only if $T$ preserves them.