Nonabelian cocycles and the spectrum of a symmetric monoidal category

Antonio M Cegarra

doi:10.3906/mat-1905-91

Abstract

We present an Eilenberg-MacLane-type description for the first, second and third spaces of the spectrum defined by a symmetric monoidal category.

Highlights

The homotopy theory of categorical structures is nowadays a relevant part of the machinery in algebraic topology and algebraic K -theory
We present an Eilenberg–MacLane-type description for the first, second and third spaces of the spectrum defined by a symmetric monoidal category
When a small category A is equipped with a symmetric monoidal structure, the group completion of its classifying space BA is an infinite loop space

Summary

Introduction

The homotopy theory of categorical structures is nowadays a relevant part of the machinery in algebraic topology and algebraic K -theory. The set Z1(C, A ) is pointed by the zero 1 -cocycle 0 = (10, 0) , which is defined by 0(c) = 0 , for any object c of C , and 10(σ) = 10 , for any morphism σ of C .

Results

Conclusion