#
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.

http://www.tac.mta.ca/tac/volumes/37/17/37-17.pdf

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