Music

So this is the thing, is this into here from somewhere?

So a closure operator, do you have it?

Perhaps you have it somewhere?

I know several examples from the Havis, and we also treated them in a formal manner into a Ledis-Guby range.

And I think this semester is also Ledis-Guby, like, in...

But they don't say that it's a woman?

No.

Do they?

Okay.

So, R.

Okay, so we have these...

So we have these three properties, which were that...

What is it?

X to the tx.

T to the x, and...

X to the y.

See what?

And then we have to verify that this yields a moment.

And the central observation is basically that...

If I have a poset as a category, then between every two objects, there is at most one morphism.

So every diagram I can draw in that category will automatically commute.

So basically the only thing you have to prove for this exercise is that all the morphisms that you need for the diagrams, the same effect exists.

The existence of a morphism is precisely that there is the actual meaning of what it is.

Okay?

So...

So the morphisms are...

X to the x, and...

So you decided to do it with mu and nu, right?

Yeah.

So what I just said is that...

Well, the existence of a morphism is just saying that...

That we have the corresponding inequalities.

And if we look at the properties of the closure operator, we see that this one checks out, and this one checks out as well.

Because, well, equality...

Since they are equal, we can just take identity from that element, and that is a morphism, so we get this morphism.

The identity of the x.

So, and then what I said is that...

All the diagrams will automatically commute.

So...

Right, so that was the... that was the assist, I guess.

I wonder maybe we missed something. Oh, that's...

So we do not even really need the...

Well, we needed... So this...

So I have our algorithm, basically it just states that t is an endopartheid.

Yes, but that might be probable from previous monads.

Because if you show that it's a monad, a monad is an endopartheid.

Ah, right, okay. But that you didn't say.

So if you take this definition as new and new, then you need to argue that...

Well, to check that it's an endopartheid, because...