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 Title: Stabilizing spectral functors of exact categories Author(s): Villeta-Garcia, Juan S Director of Research: McCarthy, Randy Doctoral Committee Chair(s): Ando, Matthew Doctoral Committee Member(s): Rezk, Charles; Malkiewich, Cary Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Algebraic K-theory Goodwillie calculus Homotopy theory Algebraic topology Abstract: 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. Issue Date: 2017-07-13 Type: Text URI: http://hdl.handle.net/2142/98290 Rights Information: Copyright 2017 Juan Villeta-Garcia Date Available in IDEALS: 2017-09-292019-09-30 Date Deposited: 2017-08
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