Claudia Scheimbauer: The Waldhausen construction and 2-Segal spaces
Time: Tue 2017-05-09 13.15 - 15.00
Location: Room 3721, Lindstedtsvägen 25, 7th floor, Department of mathematics, KTH
Participating: Claudia Scheimbauer (Oxford University)
ABSTRACT: The notion of a 2-Segal objects was introduced by Dyckerhoff and Kapranov to encode the structure of Hall algebras, and discovered independently, under the name of decomposition spaces, by Galvez-Kock-Tonks. Waldhausen's S-construction gives examples of such and we will explain that a slight variant thereof leads to an equivalent description in terms of certain "stable" double categories. I will discuss some examples, e.g. arising from bordism categories with genus constraints, and an analog of the twisted arrow category in this setting. Finally, if time permits I will give an outlook on a homotopical version.