In this paper we develop a 2-categorical approach to coherence in compact closed categories. Our approach allows us to place compact closed categories within the context of homotopical algebra. More precisely, we construct two new model categories whose fibrant objects are (two different models of) compact closed categories. We prove a strictification theorem by showing a Quillen equivalence between the two.
Keywords: Compact closed categories, coherently compact closed categories, Segal's Nerve functor
2020 MSC: 18M05, 18M60, 18N55, 18F25, 55P42, 19D23
Theory and Applications of Categories, Vol. 37, 2021, No. 37, pp 1222-1261.