Higher Segal structures in algebraic -theory
T Poguntke - arXiv preprint arXiv:1709.06510, 2017 - arxiv.org
We introduce higher dimensional analogues of simplicial constructions due to Segal and
Waldhausen, respectively producing the direct sum and algebraic $ K $-theory spectra of an …
Waldhausen, respectively producing the direct sum and algebraic $ K $-theory spectra of an …
A multiplicative comparison of Segal and Waldhausen K-theory
AM Bohmann, AM Osorno - Mathematische Zeitschrift, 2020 - Springer
In this paper, we establish a multiplicative equivalence between two multiplicative algebraic
K-theory constructions, Elmendorf and Mandell's version of Segal's K-theory and Blumberg …
K-theory constructions, Elmendorf and Mandell's version of Segal's K-theory and Blumberg …
2-Segal maps associated to a category with cofibrations
TN Carawan - arXiv preprint arXiv:2405.11561, 2024 - arxiv.org
Waldhausen's $ S_\bullet $-construction gives a way to define the algebraic $ K $-theory
space of a category with cofibrations. Specifically, the $ K $-theory space of a category with …
space of a category with cofibrations. Specifically, the $ K $-theory space of a category with …
KK-theory of C*-categories and the analytic assembly map
PD Mitchener - arXiv preprint math/0202037, 2002 - arxiv.org
arXiv:math/0202037v2 [math.KT] 23 Apr 2002 Page 1 arXiv:math/0202037v2 [math.KT] 23 Apr
2002 KK-theory of C ∗ -categories and the analytic assembly map Paul D. Mitchener email …
2002 KK-theory of C ∗ -categories and the analytic assembly map Paul D. Mitchener email …
A universal characterization of higher algebraic K-theory
AJ Blumberg, D Gepner, G Tabuada - Geometry & Topology, 2013 - msp.org
In this paper we establish a universal characterization of higher algebraic K–theory in the
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …
Algebraic proofs of some fundamental theorems in algebraic -theory
T Harris - arXiv preprint arXiv:1311.5162, 2013 - arxiv.org
arXiv:1311.5162v1 [math.KT] 20 Nov 2013 Page 1 arXiv:1311.5162v1 [math.KT] 20 Nov 2013
ALGEBRAIC PROOFS OF SOME FUNDAMENTAL THEOREMS IN ALGEBRAIC K-THEORY TOM …
ALGEBRAIC PROOFS OF SOME FUNDAMENTAL THEOREMS IN ALGEBRAIC K-THEORY TOM …
Algebraic K-theory and abstract homotopy theory
AJ Blumberg, MA Mandell - Advances in Mathematics, 2011 - Elsevier
We decompose the K-theory space of a Waldhausen category in terms of its Dwyer–Kan
simplicial localization. This leads to a criterion for functors to induce equivalences of K …
simplicial localization. This leads to a criterion for functors to induce equivalences of K …
[HTML][HTML] Spectral Mackey functors and equivariant algebraic K-theory (I)
C Barwick - Advances in Mathematics, 2017 - Elsevier
Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as
defined by Dress. We show that they can be described as excisive functors on a suitable∞ …
defined by Dress. We show that they can be described as excisive functors on a suitable∞ …