2016/12/12 by Kuber, Amit, Rosický, Jiří
#03G30 #18C10 #18C35 #18E10 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1612.03711
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are precisely the finite-injectivity classes. We prove a 2-duality between the 2-category of small exact categories and the 2-category of definable categories, and provide a new proof of its additive version. We further introduce a third vertex of the 2-category of regular toposes and show that the diagram of 2-(anti-)equivalences between three 2-categories commutes, the corresponding additive triangle is well-known.