Spectra of small categories and infinite loop space machines (Q864990)

The paper is a continuation of a series publications [J. Pure Appl. Algebra 167, No.~2--3, 301--314 (2002; Zbl 1009.18012), Topology Appl. 119, No.~1, 41--51 (2002; Zbl 0993.55004), Appl. Categ. Struct. 11, No.~2, 207--218 (2003; Zbl 1024.18006), \(K\)-Theory 36, No.~3--4, 209--222 (2005; Zbl 1117.55019)] in which the author developed various aspects of the homotopy theory of small categories. This homotopy theory is built around the strong notion of homotopy of functors, i.e. where functors are homotopic if and only if they are linked by a zig-zag of natural transformations. The present article describes how certain concepts of stable homotopy theory can be translated into this context. The author defines a spectrum of small categories and shows that the machinery of special \(\Gamma\)-spaces of Segal can be applied to construct such spectra.