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On toposes, algebraic theories, semi-abelian categories and compact Hausdorff spaces
Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 363-381.

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In this paper we study the categories C_*^op and (C_*^op)^T of T-models in C^op for an arbitrary algebraic theory T, when C is a topos or the category CHaus of compact Hausdorff spaces. It is well-known that, when C is a topos, C^op is semi-abelian. We show that CHaus_*^op is semi-abelian, as well as (CHaus_*^op)^T, and that, when C is a topos having locales of subobjects, (C_*^op)^T is also semi-abelian. In addition, we prove the representability of actions in CHaus_*^op.
Publié le :
Classification : 18B25, 18C10, 18E13, 54D30
Keywords: topos, algebraic theory, homological category, semi-abelian category, compact Hausdorff space, actions 
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Francis Borceux; Maria Manuel Clementino. On toposes, algebraic theories, semi-abelian categories and compact Hausdorff spaces. Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 363-381. http://geodesic.mathdoc.fr/item/TAC_2025_43_a10/