Stabilizing spectral functors of exact categories

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

Villeta-Garcia, Juan S

关键词: Algebraic K-theory;    Goodwillie calculus;    Homotopy theory;    Algebraic topology;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/98290/VILLETA-GARCIA-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.