2019/02/25 by Di Liberti, Ivan, González, Julia Ramos
#18B25 #18C10 #18C30 #18C35 #18D05 #18F10 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.09391
Let κ be a regular cardinal. We study Gabriel-Ulmer duality when one restricts the 2-category of locally κ-presentable categories with κ-accessible right adjoints to its locally full sub-2-category of κ-presentable Grothendieck topoi with geometric κ-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category of the 2-category of κ-small cocomplete categories with κ-colimit preserving functors arising as the corresponding 2-category of presentations via the restriction. We analyse the relation of these presentations of Grothendieck topoi with site presentations and we show that the 2-category of locally κ-presentable Grothendieck topoi with geometric κ-accessible morphisms is a reflective sub-bicategory of the full sub-2-category of the 2-category of sites with morphisms of sites genearated by the weakly κ-ary sites in the sense of Shulman [37].