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Bryce Clarke (Nov 23 2022 at 10:42):Does anyone know where the terminology "Fibrant double category" was first used to refer to a double category with all companions and conjoints?
Nathanael Arkor (Nov 23 2022 at 15:28):I suspect it was coined by @Mike Shulman (see here, for instance), the terminology being motivated by Theorem 4.1 of his paper Framed bicategories and monoidal fibrations (though I believe the terminology doesn't appear there). But Mike is the person to ask.
Mike Shulman (Nov 23 2022 at 16:22):I certainly started using it at some point with that motivation. I think that others may also have introduced it independently.
Bryce Clarke (Nov 24 2022 at 09:54):Thanks @Nathanael Arkor and @Mike Shulman . It seems like the earliest reference I could find was Mike's preprint Constructing symmetric monoidal bicategories dated April 2010.
Dylan Braithwaite (Nov 24 2022 at 10:09):There's a use of the term for a slightly weaker notion in The low-dimensional structures formed by tricategories which appeared on arxiv in 2007. They use 'fibrant double category' to mean a double category where (dom, cod) is an isofibration.
Nathanael Arkor (Nov 24 2022 at 18:56):Bryce Clarke said:
Thanks Nathanael Arkor and Mike Shulman . It seems like the earliest reference I could find was Mike's preprint Constructing symmetric monoidal bicategories dated April 2010.
The n-Category Café comment I linked is an earlier reference, but presumably you'd rather cite a paper than a blog comment :)
Bryce Clarke (Nov 24 2022 at 20:18):Nathanael Arkor said:
Bryce Clarke said:
Thanks Nathanael Arkor and Mike Shulman . It seems like the earliest reference I could find was Mike's preprint Constructing symmetric monoidal bicategories dated April 2010.
The n-Category Café comment I linked is an earlier reference, but presumably you'd rather cite a paper than a blog comment :)
Unless I'm mistaken, the comment is dated September 2010, which would be later? But in any case, a paper citation is my preference. Thanks again :)
Nathanael Arkor (Nov 24 2022 at 23:24):Bryce Clarke said:
Unless I'm mistaken, the comment is dated September 2010, which would be later? But in any case, a paper citation is my preference. Thanks again :)
Yes, I mixed up the blog post date with the comment date :sweat_smile: