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SUMMARY:Thomas Nikolaus (Westfälische Universität Münster)
DTSTART:20210203T100000Z
DTEND:20210203T113000Z
DTSTAMP:20260417T091628Z
UID:OWHHS2021/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWHHS2021/7/
 ">Polynomial functors and K-theory</a>\nby Thomas Nikolaus (Westfälische 
 Universität Münster) as part of Opening Workshop (IRP Higher Homotopy St
 ructures 2021\, CRM-Bellaterra)\n\n\nAbstract\nWe will report on (long ove
 rdue) joint work with Clark Barwick\, Saul Glasman and Akhil Mathew. Algeb
 raic $K$-theory of a ring or more generally an additive category is\, by i
 ts definition as a group completion\, functorial in additive functors. We 
 prove that it is in fact functorial in more functors: the so-called polyno
 mial functors (in the sense of Eilenberg–Mac Lane) and still satisfies a
  universal property. This generalizes previous results by Passi\, Dold and
  others. We will in fact show this for a stable $\\infty$-category and pol
 ynomial ($= n$-excisive) functors in the sense of Goodwillie. If time perm
 its\, we will explain applications of this result for lambda-ring structur
 es on algebraic $K$-theory and give the definition of a spectral lambda ri
 ng (i.e.\, a higher algebra version of a lambda ring).\n
LOCATION:https://researchseminars.org/talk/OWHHS2021/7/
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