2024/10/03 by Kern, David
#18N65 #55P42 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.02578
Lessard's ℤ-categories are an analogue of ω-categories possessing cells in all positive and negative dimensions. Categorical spectra, developed by Stefanich, are an analogue of spectra obtained by replacing the suspension of pointed ∞-groupoids by that of pointed (∞,ω)-categories. We give an ∞-categorical definition of weak ℤ-categories (alias (∞,ℤ)-categories), and show categorical spectra to be equivalent to pointed (∞,ℤ)-categories. In particular, we show that the stable cells of categorical spectra coincide with the natural cells of (∞,ℤ)-categories, and recover Lessard's description of spectra as pointed weak ℤ-groupoids.