anafunctors

anafunctors

[categories]

Date: Wed, 29 Jan 1997 14:56:30 -0500 (EST)
From: Michael Makkai <makkai@triples.math.mcgill.ca>

John Baez asked, on January 24, about anafunctors. As far as I know, the
notion was first explicitly introduced in my paper "Avoiding the axiom of
choice in general category theory", in JPAA 108 (1996), 109-173. The term
was suggested by Dusko Pavlovic. Precursors occur in the work of Max
Kelly, and Andre Joyal, as I explain in the paper. The concept John gives
is equivalent to "saturated anafunctor" in the paper; plain anafunctor is
something that generalizes "functor". The wording of the definition of
"saturated anafunctor" is different from John's definition, but the
equivalence is fairly straightforward. I should mention that John`s
definition is a very useful formulation, especially when one wants to
generalize things to higher dimensional categories, as I came to realize
some time after I started studying the John Baez/James Dolan announcement
on weak n-categories. 

In addition to the paper mentioned above, there is reference to
anafunctors in "First Order Logic with Dependent Sorts", a monograph that
will appear in Springer's Lecture Notes in Logic as soon as I manage to
complete the necessary revisions; it is available electronically from the
TRIPLES and HYPATIA (?) sites.

anafunctors

[categories]

Date: Thu, 23 Jan 1997 13:26:33 -0800
From: john baez <baez@math.ucr.edu>

What is the locus classicus for "anafunctors"?  As far as I know,
an anafunctor F: C -> D is a presheaf on C x D^{op} such that
F(c,.) is representable for any object c of C.  Is this how it's
normally defined?  Where is composition of anafunctors discussed?
Are there other names for these things?

John Baez