Re: Partial functors ..

[Ross Street <ross.street@mq.edu.au>]

Dear All

David Leduc’s statement: 
"A partial functor from C to D is given by a subcategory S of C and a functor from S to D.”

If this is taken as given then today I don’t want to add to what people have said.

But there is another notion of partial functor that I learnt from Brian Day
who learnt it from Bill Lawvere. If we are to replace 2 in Set by Set in Cat,
then characteristic maps C —> 2 should become presheaves C^op —> Set,
so injective functions S—> C should become discrete fibrations E —> C.
Then a partial map from C to D would be a span C <— E —> D
with C <— E a discrete fibration and E —> D any functor.
The partial map classifier is then the coproduct completion FamD
of D. Add size restrictions, to taste.

Ross



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