Fortunately, it is known that every monoidal category is equivalent to a strict one [MacL, Ch.
Derived equivalences and sl_2-categorifications for U_q(gl_n)
Lusztig, Introduction to Quantum Groups, Progress in Mathematics 110, Birkhauser, Boston MA (1993). [MacL] S.
Derived equivalences and sl_2-categorifications for U_q(gl_n)
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