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Topics in algebraic and topological K-theory
(Springer, 2011)
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison ...
On the K-theory of Z-categories
(arXiv, 2022)
We relate the notions of Noetherian, regular coherent and regular n-coherent category for Z-linear categories with finite objects with the corresponding notions for unital rings. We use this relation to obtain a vanishing ...
On the Classification of Almost Square-Free Modular Categories
(Springer, 2017-11)
Let (Formula presented.) be a modular category of Frobenius-Perron dimension dqn, where q > 2 is a prime number and d is a square-free integer. We show that (Formula presented.) must be integral and nilpotent and therefore ...
From model to quasi-categories
(Universidade Federal de Minas GeraisBrasilICX - DEPARTAMENTO DE MATEMÁTICAPrograma de Pós-Graduação em MatemáticaUFMG, 2022-02-22)
Esta dissertação é uma humilde introdução a grandes ferramentas da teoria da homotopia abstrata: categorias modelo e ∞-categorias (através de quasicategorias). A primeira parte do texto apresenta estas estruturas, conectando ...
Universal coefficient theorem in triangulated categories
(Springer Verlag Berlín, 2008-04)
We consider a homology theory Open image in new window on a triangulated category Open image in new window with values in an abelian category Open image in new window . If the functor h reflects isomorphisms, is full and ...
Some equivalences between homotopy and derived categories
(Universidad de AllahabadÁlgebra Teoría de Números y Aplicaciones: ERMÁlgebra U de AAllahabad, India, 2022)
Group actions on 2-categories
(Springer, 2019-05)
We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories ...
Every rig with a one-variable fixed point presentation is the burnside rig of a prextensive category
(Springer, 2017-08)
We extend the work of Schanuel, Lawvere, Blass and Gates in Objective Number Theory by proving that, for any L(X) ∈ N[X], the rig N[X]/(X = L(X)) is the Burnside rig of a prextensive category.