Geodesic
The canonical intensive quality of a cohesive topos
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 250-279 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18B25, 03G30, 18F99
Keywords: Axiomatic Cohesion, Topos theory, Geometric morphisms, Intensive quality 
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     author = {F. Marmolejo and M. Menni},
     title = {The canonical intensive quality of a cohesive topos},
     journal = {Theory and applications of categories},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a8/}
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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/