新着情報

代数特別セミナー

投稿日時 : 2018/09/27

日時: 10月15日 16:00-17:30

場所: D814

講演者: Andrew William Macpherson (IPMU)

題目: A Yoneda philosophy of correspondences
Abstract: Cohomology is bivariant, which means that to a morphism f it associates not only a pullback map f^*, but also (under certain conditions) an Umkehr map in the opposite direction. These maps satisfy a "push-pull" or "base change" identity. Everyone knows that this implies that cohomology can be thought of as a functor out of a certain category CORR of "correspondences", whose morphisms are "rooves" and whose composition law is defined by taking a fibre product of kernels.

In higher category theory, specifying objects by describing the morphism spaces and composition law explicitly --- as we just did with correspondences --- is rather inconvenient. Rather, it is better to define things via their universal properties. In this talk, I will give a universal interpretation for CORR in terms of "bivariant functors" into an (∞,2)-category, which takes out the pain from constructing functors out of CORR.

連絡先: 木村健一郎