The creative power of categories: elements of History and some new perspectives

Abstract: The notion of category and the basic language of category theory (functors, natural transformation of functors, limits, colimits, adjoint functors,...) are very recent in History and may seem too simple and too general.

However, it has been proved repeatedly - especially by Grothendieck and his followers - that these simple notions can be transformed into very powerful means of creation of new mathematics.

The purpose of this talk will be to present some of the most powerful category-based ideas and theories introduced by Grothendieck. Some emphasis will be given to the notion of topos, which Grothendieck considered its most important idea (together with the idea of motive) and which recently has been given new impetus by Italian mathematician Olivia Caramello's "technique of toposes as bridges".

Mathematics

Audience: researchers in the topic

IPM-Isfahan Mathematics Colloquium