Re: Partial functors ..

[Steve Lack <steve.lack@mq.edu.au>]

Dear Ross,

I think you meant the *product* completion Fam(D*)*. 
If you use the coproduct completion, then you need to use discrete *opfibrations* and covariant Set-valued functors.

There are some details in the appendix to our joint paper “The formal theory of monads II”.

Steve.

> On 18 Mar 2015, at 11:47 am, Ross Street <ross.street@mq.edu.au> wrote:
> 
> 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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