* Strictifying normal lax functors
@ 2011-09-20 9:10 Jonathan CHICHE 齊正航
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From: Jonathan CHICHE 齊正航 @ 2011-09-20 9:10 UTC (permalink / raw)
To: Categories list
Dear all,
Given a 2-category C, there is a 2-category C' and a normal lax
functor from C to C' such that, for any normal lax functor from C to
a 2-category D, there is a unique strict 2-functor from C' to D which
makes the triangle commute. (To avoid any confusion: I take normal
lax functor to be what is defined in, say, p. 7 of the paper http://
arxiv.org/abs/0909.4229.)
Gray, in "Formal Category Theory", I,4.23, Appendix A (p. 92), gives
an analogous universal construction with respect to general oplax
functors, and refers the reader to Bénabou's unpublished lectures as
a more general reference. I have seen a reference to Theorem 3.13 of
the Blackwell-Kelly-Power paper "Two-dimensional monad theory" (JPAA
59 (1989, 1-41), thanks to Matias del Hoyo for pointing that to me),
but I do not have it handy and I am unsure whether the general
theorem provides a much concrete description of the universal 2-
category in the particular case I am interested in (and I do not know
whether the normalized case falls into its range of application).
Are there references dealing specifically with normalized (op)lax
functors? Is there an explicit description of this universal
construction I could refer to in the literature?
Thanks in advance!
Best wishes,
Jonathan
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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