Zobrazeno 1 - 10
of 390
pro vyhledávání: '"18F25"'
In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the scissors congruen
Externí odkaz:
http://arxiv.org/abs/2408.08081
Autor:
Küng, Felix
We introduce the notion of Grothendieck heaps for unpointed Waldhausen categories and unpointed stable $\infty$-categories. This allows an extension of the studies of $\mathrm{K}_0$ to the homotopy category of unpointed topological spaces.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/2407.20911
In this paper we extend equivariant infinite loop space theory to take into account multiplicative norms: For every finite group $G$, we construct a multiplicative refinement of the comparison between the $\infty$-categories of connective genuine $G$
Externí odkaz:
http://arxiv.org/abs/2407.08399
Autor:
Ogawa, Yasuaki, Shah, Amit
Waldhausen categories were introduced to extend algebraic $K$-theory beyond Quillen's exact categories. In this article, we modify Waldhausen's axioms so that it matches better with the theory of extriangulated categories, introducing a weak Waldhaus
Externí odkaz:
http://arxiv.org/abs/2406.18091
Autor:
Matsukawa, Hisato
In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application demonstrates that co
Externí odkaz:
http://arxiv.org/abs/2405.03498
Autor:
Kranz, Julian, Nishikawa, Shintaro
We develop general methods to compute the algebraic $K$-theory of crossed products by Bernoulli shifts on additive categories. From this we obtain a $K$-theory formula for regular group rings associated to wreath products of finite groups by groups s
Externí odkaz:
http://arxiv.org/abs/2401.14806
We provide a unifying approach to different constructions of the algebraic $K$-theory of equivariant symmetric monoidal categories. A consequence of our work is that every connective genuine $G$-spectrum is equivalent to the equivariant algebraic $K$
Externí odkaz:
http://arxiv.org/abs/2312.04705
We prove the fibred Farrell--Jones Conjecture (FJC) in $A$-, $K$-, and $L$-theory for a large class of suspensions of relatively hyperbolic groups, as well as for all suspensions of one-ended hyperbolic groups. We deduce two applications: (1) FJC for
Externí odkaz:
http://arxiv.org/abs/2311.14036
Autor:
Saunier, Victor
We show that Quillen's resolution theorem for K-theory also applies to exact $\infty$-categories. We introduce heart structures on a stable $\infty$-category, generalizing weight structures, and using resolution ideas, we show that the category of st
Externí odkaz:
http://arxiv.org/abs/2311.13836
Autor:
Ogawa, Yasuaki, Shah, Amit
Publikováno v:
J. Algebra 658:450-485 (2024)
Quillen's Resolution Theorem in algebraic $K$-theory provides a powerful computational tool for calculating $K$-groups of exact categories. At the level of $K_0$, this result goes back to Grothendieck. In this article, we first establish an extriangu
Externí odkaz:
http://arxiv.org/abs/2311.10576