Thursday, September 30, 14:00, 7.527

Simone Virili (Barcelona), Locally finitely presented Grothendieck categories with a flat generator,

Abstract:
[This is a joint project with Lorenzo Martini, Carlos E. Parra and Manuel Saorín]

A problem raised by Cuadra and Simson in 2007 asks whether a locally finitely presented Grothendieck category with enough flat objects has enough projective objects. We prove that these categories are precisely the locally finitely presented Grothendieck categories with exact products. This enables reformulations of the problem, showing relations to a classical problem posed by Miller in 1975 and to the Telescope Conjecture for compactly generated triangulated categories. We will conclude by describing a concrete counter-example to one of these reformulations, thus also proving that the Cuadra and Simson's problem has a negative solution in general.