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Coherence for invertible objects and multigraded homotopy rings

Daniel Dugger
Algebraic & Geometric Topology 14 (2014) 1055–1106
DOI: 10.2140/agt.2014.14.1055
Abstract

We prove a coherence theorem for invertible objects in a symmetric monoidal category (or equivalently, a coherence theorem for symmetric categorical groups). This is used to deduce associativity, skew-commutativity, and related results for multigraded morphism rings, generalizing the well-known versions for stable homotopy groups.

Keywords
coherence, invertible object, symmetric monoidal
Mathematical Subject Classification 2010
Primary: 18D10
Secondary: 55Q05, 55U99
References
Publication
Received: 5 March 2013
Revised: 8 October 2013
Accepted: 9 October 2013
Published: 21 March 2014
Authors
Daniel Dugger
Department of Mathematics
University of Oregon
Fenton Hall
Eugene, OR 97403
USA
http://math.uoregon.edu/~ddugger