In this paper we study the categories \( \mathcal C_*^{\mathsf{op}} \) and \( (\mathcal C_*^{\mathsf{op}})^{\mathbb T} \) of \( \mathbb T \)-models in \( \mathcal C_*^{\mathsf{op}} \) for an arbitrary algebraic theory \( \mathbb T \), when \( \mathcal C \) is a topos or the category \( \mathsf{CHaus} \) of compact Hausdorff spaces. It is well-known that, when \( \mathcal C \) is a topos, \( \mathcal C_*^{\mathsf{op}} \) is semi-abelian. We show that \( \mathsf{CHaus}_*^{\mathsf{op}} \) is semi-abelian, as well as \( (\mathsf{CHaus}_*^{\mathsf{op}})^{\mathbb T} \), and that, when \( \mathcal C \) is a topos having locales of subobjects, \( (\mathsf{CHaus}_*^{\mathsf{op}})^{\mathbb T} \) is also semi-abelian. In addition, we prove the representability of actions in \( \mathsf{CHaus}_*^{\mathsf{op}} \).