Re: Partial functor

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

Dear David,

There are many possible meanings of partial morphism between categories,
depending on  what meaning you attach to "subcategory". Different meanings
will be appropriate depending on the applications in question.

One possibility, which I believe was first considered by Lawvere, is to take "subcategory" 
of C to be a discrete opfibration over C. The resulting 2-category is described in 
detail in the appendix of 

Stephen Lack and Ross Street, The formal theory of monads II, JPAA 175:243-265, 2002.

where it is also shown that these partial maps are classified, in a suitable sense,
by the Fam construction. 

Regards,

Steve Lack.


On 07/11/2011, at 11:55 PM, david leduc wrote:

> Hi,
> 
> A partial functor from C to D is given by a subcategory S of C and a
> functor from S to D. What is the appropriate notion of natural
> transformation between partial functors that would allow to turn small
> categories, partial functors and those "natural transformations" into
> a bicategory? The difficulty is that two partial functors from C to D
> might not have the same definition domain.
> 

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