An issue with Christopher King's proposal, below, is what to do for a map between an object of S and an object of C not in S. Cheers, -- Fred --- ------ Original Message ------ Received: Mon, 16 Mar 2015 08:59:05 AM EDT From: Christopher King <G.nius.ck@gmail.com> To: <categories@mta.ca> Subject: categories: Re: Partial functor
David Leduc <david.leduc6 <at> googlemail.com> writes:
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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I know this is late, but I find a quite obvious notion for it. Why not turn your partial functor into a regular functor from C->D+1 (1 and + are the terminal object and coproduct in the category of categories.) Now you can just use regular natural transformations.
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