BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Olivia Caramello (Università dell'Insubria) DTSTART:20210615T123000Z DTEND:20210615T133000Z DTSTAMP:20260423T021233Z UID:itaca/5 DESCRIPTION:Title: Re lative topos theory via stacks\nby Olivia Caramello (Università dell' Insubria) as part of ItaCa Fest 2021\n\n\nAbstract\nIn this talk\, based o n joint work with Riccardo Zanfa\, we shall introduce new foundations for relative topos theory based on stacks. One of the central results in our t heory is an adjunction between the category of (relatively small) toposes over the topos of sheaves on a given site (C\, J) and that of C-indexed ca tegories. This represents a wide generalization of the classical adjunctio n between presheaves on a topological space and bundles over it\, and allo ws one to interpret several constructions on sheaves and stacks in a geome trical way\; in particular\, it leads to fibrational descriptions of direc t and inverse images of sheaves and stacks\, as well as to a geometric und erstanding of the sheafification process. It also naturally allows one to regard any Grothendieck topos as a ‘petit’ topos associated with a ‘ gros’ topos\, thereby providing an answer to a problem posed by Grothend ieck in the seventies.\n LOCATION:https://researchseminars.org/talk/itaca/5/ END:VEVENT END:VCALENDAR