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Shea Levy (Oct 15 2020 at 16:44):Given , is there some word that can refer to either A or B or both? An "endpoint" of f maybe?
Chad Nester (Oct 15 2020 at 16:53):(co)domain :stuck_out_tongue:
Matteo Capucci (he/him) (Oct 15 2020 at 16:55):Boundary?
Matteo Capucci (he/him) (Oct 15 2020 at 17:08):(This terminology is grounded in the simplicial pov on categories)
Matteo Capucci (he/him) (Oct 15 2020 at 17:08):(Not that it makes it better, though)
Matteo Capucci (he/him) (Oct 15 2020 at 17:08):(In fact I like Chad's better :laughing: )
Reid Barton (Oct 15 2020 at 17:08):When would you use this term?
Chad Nester (Oct 15 2020 at 17:15):I actually use "boundary" when I'm drawing string diagrams, since in this case it's literally one of the boundaries of the diagram.
Matteo Capucci (he/him) (Oct 15 2020 at 17:15):Oh right, in that context is perfect
Fabrizio Genovese (Oct 15 2020 at 17:57):To my knowledge in standard category theory and are called source and target, respectively. Domain and codomain are also acceptable, even if those are mainly preferred when working with sets and functions.
David Michael Roberts (Oct 15 2020 at 22:25):I sometimes use 'source/target' to refer to A and B together (better, imho, than (co)domain)
sarahzrf (Oct 16 2020 at 00:55):Fabrizio Genovese said:
To my knowledge in standard category theory and are called source and target, respectively. Domain and codomain are also acceptable, even if those are mainly preferred when working with sets and functions.
personally i say domain/codomain much more often than source/target no matter what kind of category i'm working with :thinking:
Fabrizio Genovese (Oct 17 2020 at 10:02):Me too. But according to MacLane "source/target" is the preferred terminology, if I recall correctly
Fawzi Hreiki (Oct 17 2020 at 10:20):If I recall correctly, Mac Lane uses the ‘source/target’ terminology when talking about graphs
Fawzi Hreiki (Oct 17 2020 at 10:21):But then switches mostly to domain and codomain when talking about categories proper
Fawzi Hreiki (Oct 17 2020 at 10:22):I think the source/target terminology usually signifies that the categories being dealt with are ‘geometric’ or ‘small’ in some way
Fawzi Hreiki (Oct 17 2020 at 10:22):For example with internal categories
Jules Hedges (Oct 17 2020 at 10:48):Clearly it should be "the blunt end" and "the pointy end"
David Michael Roberts (Oct 18 2020 at 07:29):Fawzi Hreiki said:
I think the source/target terminology usually signifies that the categories being dealt with are ‘geometric’ or ‘small’ in some way
This feels like the sort of thing done by people who define a groupoid to be a small category with all arrows invertible.
Morgan Rogers (he/him) (Oct 18 2020 at 09:51):domain/codomain captures the duality nicely. A morphism in the dual of a category goes from its codomain to its cocodomain :wink: