Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Created lax-idempotent 2-monad, with some definitions from Kelly–Lack. I think Kock has a couple of others. I’ll add more, like proofs of the equivalence of the definitions, and more on the cocompletion example, later (next week, probably).
Nice, thank you! One quibble: the “idea” description (“algebras over any given object are essentially unique if they exist”) is really the idea of a property-like 2-monad, which is a more general concept than a lax-idempotent one.
Right, good point. I’ve edited that section a bit – what do you think of it now?
Looks good.
I added some details to the page last night, but for some reason it didn’t turn up in the/my RSS feed, so I thought I’d drop a note here.
Thanks!
I would like to ask you to drop a note here in any case, when you add something. That facilitates interaction a lot more, I think.
Nice, thank you! And I second what Urs said.
I would like to ask you to drop a note here in any case, when you add something. That facilitates interaction a lot more, I think.
OK, will do.
Right, I think I’m done with this for the time being, unless anyone has any suggestions. I’ve finished off the proof (taken from Kelly & Lack’s paper) of the equivalence of the two usual definitions (unique-2-cell and adjoint-to-unit), and I’ve mentioned colax-idempotence with the fibration 2-monad as an example.
Thanks! I added a reference to generalized multicategories, which are one nice source of lax-idempotence.
Probably property-like structure deserves its own page eventually, where we can discuss property-like 2-monads.
1 to 10 of 10