Seminar: Towards a theory of classification: general setting by George Elliott (University of Toronto)
- Speaker: Prof. George Elliott (University of Toronto)
- Date: Wednesday, February 27th
- Time: 14:00-16:00
- Venue: C210, OIST Center building
Title: Towards a theory of classification: general setting
An abstract classifying invariant—a functor!—for a certain kind of given category is constructed by passing to equivalence classes of morphisms, which themselves form a category. Thus, the objects are the same, but the classifying category—so named because isomorphism of objects downstairs implies isomorphism upstairs—is typically much simpler than the given one, as many morphisms are identified by the classification functor, and many automorphisms killed. (Note that one cannot just replace objects by isomorphism classes, as one doesn’t get a category this way.) The classifying category is a priori an abstract one, but, perhaps surprisingly, in interesting cases, its Yoneda concretization becomes spectacularly simple.