Parsummable categories as a strictification of symmetric monoidal categories

Tobias Lenz

We prove that the homotopy theory of parsummable categories (as defined by Schwede) with respect to the underlying equivalences of categories is equivalent to the usual homotopy theory of symmetric monoidal categories. In particular, this yields a model of symmetric monoidal categories in terms of categories equipped with a strictly commutative, associative, and unital (but only partially defined) operation.

Keywords: Symmetric monoidal categories, parsummable categories, strictification, global algebraic K-theory

2020 MSC: Primary 18D10, 18D35, Secondary 19D23, 18G55

Theory and Applications of Categories, Vol. 37, 2021, No. 17, pp 482-529.

Published 2021-05-12.

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