You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
James Deikun (Mar 27 2025 at 14:54):Why do people use extendable algebraic patterns when polynomial -monads are conceptually simpler and have the more clearly interesting generalization of -monads in general? Is it similar to the reason Lurie defined -operads as -categories equipped with a certain kind of functor to pointed sets, i.e., it's just easier to compute with?
daniel gratzer (Mar 27 2025 at 21:27):I suspect a combination of easier to compute with (an algebraic pattern is usually a fairly small and concrete category with a useful factorization system) and easier to construct. It's also sometimes helpful that symmetric monoidal categories are a particular algebraic pattern (in much the same way the fact that this is useful for $\infty$-operads). Also, I tend to think of algebraic patterns as a bit simpler than polynomial monads, so it's a matter of perspective and taste as well :)
Also, nice algebraic patterns are more structured than an arbitrary polynomial monads (I believe that they correspond to complete ones).