#monads

[algebraic-dualist]

Me getting started on the next chapter of the category theory textbook I am writing............

[nicuveo]

I forgot to post it here! This is something i had been meaning to write or talk about for a long while, but i've made it a youtube essay instead, as an experiment, to learn something new.

In short: what the hell is the problem with monads? Where does that problem come from? And how do we fix it?

This is my first attempt at doing something like this, all feedback welcome!

[maplecinnamonbun]

(f <=< g) Nothing

None monad with left fish

[dressedsalad]

I have a Category theory question, I'll answer this myself when i have time but i'll see if someone can quickly confirm or deny it first.

I know that if a monad T over a cocomplete & complete & locally small category C that preserves filtered colimits then the category of T-algebras is cocomplete.

The proof does some funny constructions by creating a huge chain of things, to then take the colimit and use the hypothesis on T.

Now, the chain created in the proof is countable, but to me it seems plausible that, if our functor T preserves colimits over filtered diagrams with cofinality greater or equal to some fixed cardinal k, then we could continue the chain using colimits in C whenever we hit a limit ordinal, to get a chain indexed over k instead, where we can then apply the rest of the reasoning word for word.

Is this reasonable? i need to show cocompleteness/ failure of cocompleteness on some algebraic objects w infinitary operations.

[tharenia]

outfit swap!!! 🎀

[eyes-of-nine]

got the real boy ending yesterday, love this weird freak sm, would never want to be in his vicinity<33

[shinozaki-ayumi]

forgot to post this here lol. i finished LoP for the first time the other day just in time for Overture and absolutely loved it!!!!

[sanaez214]

Lies of P fan art. Sorry for late to draw about DLC. I can't wait to play it!

[venigni]

Parallels.

[casakhelone]

WIP: The Blue Companions (2023)

A sketch from 2023 of P & Sophia based off the paintings The Blue Boy (Thomas Gainsborough) and Pinkie (Thomas Lawrence).

The first image is Pinocchio's part of the portrait that I started developing during a livestream at the beginning of 2024.

[arsuf]

And now I know. ...Carlo.

     LIES OF P: OVERTURE (2025)

[algebraic-dualist]

Given a monad T on a cartesian category C recall the forgetful functor U : C^T -> C. It seems to me that we can recover the "operations" encoded by the monad by thinking of natural transformations: θ_A : U(A)^n -> U(A)

In the case that the monad T is encoding an algebraic theory on Set, it is clear that every term t(x_1, x_2, ..., x_n) induces, by evaluation, on each algebra a function t_A : A^n -> A which commutes with all T-homomorphisms. So, it would induce an element of Nat(U^n, U). Thus, we get sets Op_T(n) which we can use to assemble together an operad Op_T. Question: When are algebras of this operad encoding exactly the algebras of the monad?

[nicuveo]

Someone redeemed the "rant about monads" perk on my channel, so... here's 50 minutes of me ranting about monads and trying to convey an intuition for them. Warning: a bit loud, it's a rant after all. :D

https://www.twitch.tv/nicuveo/v/2325273076

[secteel]

The Legendary Stalker.

Finished the DLC this morning and Lea is hands down my FAVOURITE character..

[tharenia]

💙✨

[lilac-cat-draws]

Pulled an Actor AU cuz I haven't fully coped with Overture