2020/09/18 by Coley, Ian
#18F25 #18N40 #55U35 #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2009.09063
We build on work of Muro-Raptis in [Ann. K-Theory 2 (2017), no. 2, 303-340] and Cisinski-Neeman in [Adv. Math. 217 (2008), no. 4, 1381-1475] to prove that the additivity of derivator K-theory holds for a large class of derivators that we call left pointed derivators, which includes all triangulated derivators. The proof methodology is an adaptation of the combinatorial methods of Grayson in [Doc. Math. 16 (2011), 457-464]. As a corollary, we prove that derivator K-theory is an infinite loop space. Finally, we speculate on the role of derivator K-theory as a trace from the algebraic K-theory of a stable ∞-category à la Blumberg-Gepner-Tabuada in [Geom. Topol. 17 (2013), no. 2, 733-838].