Stabilizing spectral functors of exact categories

We define and study the $K$-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of McCarthy, we determine, for a discrete ring $R$, the $K$-theory of the exact category of finitely-generated projective $R$-modules with coefficients in the $n$-fold smash product functor. This computation allows us to analyze the effects of applying this functorial construction to the Goodwillie Taylor tower of a homotopy endofunctor of spectra. In the case of \Sigma^\infty\Omega^\infty, the associated tower recovers the Taylor tower of relative $K$-theory as computed by Lindenstrauss and McCarthy.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Villeta-Garcia, Juan S

Contributors dc:contributor

• McCarthy, Randy
• Ando, Matthew
• Rezk, Charles
• Malkiewich, Cary

• Algebraic K-theory
• Goodwillie calculus
• Homotopy theory
• Algebraic topology

Statement dc:rights

• Copyright 2017 Juan Villeta-Garcia

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/98290

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F98290