2 problems

Let $\mathsf{LI}$ denote the class of split epimorphisms, and let $\overline{\mathcal{S}}$ denote the class of morphisms whose associated comparison cell is an isomorphism. Write…

Let $\mathcal{U}$ be the class of morphisms satisfying $\operatorname{id}_{A}\leq f^*\cdot f$ for some $f^*$, and let \mathcal{U}^{\mathrel{\ooalign{{\wedge}\cr\hfilmid\hfil}}}…