SEMINARIO DI
MATEMATICA
ore
15.00
Scuola Normale
Superiore
Pisa
(Aula
Mancini)
F.
William Lawvere
Terrà
un seminario dal titolo:
“What
is a space”
Abstract:
A
space is just an object in a category of spaces!
The
implied further question is given a very general answer involving lextensivity,
as well as a much more structured answer involving dialectically coupled
(cohesive/discrete) pairs of toposes. Examples can be analyzed and constructed
using the simple geometric paradigm of figures and incidence relations, by which
any lextensive category can be embedded in a Grothendieck topos; more refined
subtoposes of the latter are specified by Grothendieck coverings that embody the
geometrical equivalent of existential/disjunctive conditions on these extended
spaces; a specific example involves a generalization of Maschke means. The
extended spaces always include the Hurewicz exponential spaces, for example,
spaces of functions and distributions equipped automatically with the ambient
sort of cohesion. Examples important for smooth, analytic, and algebraic
geometry are infinitesimally generated, pursuing an observation that goes back
to Euler. A smooth account of points and components for algebraic geometry over
a non‐algebraically
closed field is achieved by replacing Cantorian abstract sets with a
Galois‐Barr
topos as the discrete aspect. The basic goal is to help make the advances in
Algebraic Geometry during the past 50 years more accessible to students and to
colleagues in related fields by utilizing the simplifying advances in
categorical foundations during the same 50 years, especially guided by proposals
made by Grothendieck in 1973.
Tutti gli interessati
sono invitati a partecipare.
Classe
di Scienze