On the tensor product of well generated pretriangulated DG categories
Julia Ramos González (University of Antwerp)
Wednesday 17th October, 2018 16:00-17:00 Maths 311B
This is joint work with Wendy Lowen. Motivated by noncommutative algebraic geometry, where enhancements of triangulated categories are considered as models of (possibly) noncommutative spaces, we define a tensor product of well generated pretriangulated dg categories by means of a universal property in the homotopy category of dg categories. We first prove its existence and then provide a construction in terms of the representations of well generated pretriangulated dg categories provided by Porta's triangulated version of the Gabriel-Popescu theorem. In addition, given a regular cardinal alpha, we show that the tensor product preserves alpha-compactness. At the end of the talk we introduce some work in progress which relates this tensor product to the tensor product of Grothendieck categories as well as to Lurie's tensor product of presentable infinity-categories.