Geodesic
The canonical intensive quality of a cohesive topos
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 250-279

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We strengthen a result of Lawvere by proving that every pre-cohesive geometric morphism p: E --> S has a canonical intensive quality s: E --> L. We also discuss examples among bounded pre-cohesive p: E --> S and, in particular, we show that if E is a presheaf topos then so is L. This result lifts to Grothendieck toposes but the sites obtained need not be subcanonical. To illustrate this phenomenon, and also the subtle passage from E to L, we consider a particular family of bounded cohesive toposes over Set and build subcanonical sites for their associated categories L.

Publié le :
Classification : 18B25, 03G30, 18F99
Keywords: Axiomatic Cohesion, Topos theory, Geometric morphisms, Intensive quality 
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F. Marmolejo; M. Menni. The canonical intensive quality of a cohesive topos. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 250-279. http://geodesic.mathdoc.fr/item/TAC_2021_36_a8/