Algebraic & Geometric Topology

Coherence for invertible objects and multigraded homotopy rings

Daniel Dugger

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

coherence invertible object symmetric monoidal


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.

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