Algebraic & Geometric Topology

Coherence for invertible objects and multigraded homotopy rings

Daniel Dugger

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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.

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 2 (2014), 1055-1106.

Dates
Received: 5 March 2013
Revised: 8 October 2013
Accepted: 9 October 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715857

Digital Object Identifier
doi:10.2140/agt.2014.14.1055

Mathematical Reviews number (MathSciNet)
MR3180827

Zentralblatt MATH identifier
1312.18002

Subjects
Primary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
Secondary: 55Q05: Homotopy groups, general; sets of homotopy classes 55U99: None of the above, but in this section

Keywords
coherence invertible object symmetric monoidal

Citation

Dugger, Daniel. Coherence for invertible objects and multigraded homotopy rings. Algebr. Geom. Topol. 14 (2014), no. 2, 1055--1106. doi:10.2140/agt.2014.14.1055. https://projecteuclid.org/euclid.agt/1513715857


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