* Strictifying monoidal functors
@ 2008-05-07 6:59 David Roberts
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From: David Roberts @ 2008-05-07 6:59 UTC (permalink / raw)
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Hi all,
While we can make all monoidal categories strict, I was wondering how
strict we can make monoidal functors. More precisely, given a strong
monoidal functor F:(C,@,I) --> (D,*,1) between strict monoidal
categories, it has the data
m_xy: F(x)*F(y) ---> F(x@y) (natural)
u:1 ---> F(I).
Is F naturally isomorphic to a strong monoidal functor such that u is
the identity?
In Baez-Lauda HDA 5 it is an exercise to the reader in the proof of
Proposition 8.3.6 to do this for weak monoidal categories.
Cheers,
David
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2008-05-07 6:59 Strictifying monoidal functors David Roberts
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