 

Peter Schauenburg
Turning Monoidal Categories into Strict Ones


Published: 
November 13, 2001

Keywords: 
monoidal category, strict monoidal category 
Subject: 
18W10 


Abstract
It is wellknown that every monoidal category is equivalent to a
strict one. We show that for categories of sets with additional
structure (which we define quite formally below) it is not even
necessary to change the category: The same category has a different
(but isomorphic) tensor product, with which it is a strict
monoidal category. The result applies to ordinary (bi)modules,
where it shows that one can choose a realization of the tensor
product for each pair of modules in such a way that tensor
products are strictly associative. Perhaps more surprisingly,
the result also applies to such nontrivially nonstrict
categories as the category of modules over a quasibialgebra.


Author information
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
schauen@rz.mathematik.unimuenchen.de
http://www.mathematik.unimuenchen.de/personen/schauenburg.html

