Re: Partial functors ..

["Fred E.J. Linton" <fejlinton@usa.net>]

One had better take care to note explicitly how to compose maps to 
and from the newly adjoined "zero object", if following Yetter's idea,

> The previous suggestion of considering functors to D + 1 was a false start
> for reasons Fred and Uwe pointed out, but it suggests a better approach: 
> consider functors to the category D~ formed from D by freely adjoining a
> zero object.  Arrows not in S now have somewhere to go (the zero arrow
> with the appropriate source and target).

For, given a and b objects in D and writing z for the newly adjoined zero
object, what are we to take for compositions  a --> * --> b ? Or were we 
also to adjoin "zero maps" z_(a,b) to each existing homset D(a, b), and 
then set these compositions all equal to those new zero maps?

That suggests Yetter really meant to propose forming the free *pointed* 
category with zero object freely engendered by D ... or maybe that's what  
his words already meant to convey? Apologies if I was deaf to that tone :-) .

Cheers, -- Fred



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]