Graphic monoids and Hegelian "taco" (contd.)

0:00 These are all parameterized by the omegas of left, which are the left ideals. The left ideals are also the right ideals. The truth values, of course, of the category of application are exactly the right ideals. And, again, another amusing demonstration shows that this is actually a sub-application. In other words, the canonical action of m1 omega actually preserves the property of being left ideal. These are the right ideals, among the right ideals are the left ideals, and an action of them on the right ideals, that's reading Vichy's topos, a sort of a canonical thing, but, in fact, the left ideals are a little different, so there are these two rather remarkable facts that these sub-topos, these essential sub-topos, can actually be parameterized by certain true values. Now, just one more word. The picture is maybe a higher dimension. If I have two stages of these things, I get an eight element object called the tacho, the Galilean tacho. The Galilean because the relationship between the subtopicals is the Altabrum of Hegel. And DACO, because it looks like the kind of students that eat in northern Mexico, eat inside, and they don't. The thing is, it's actually three-dimensional. So even though I don't have a precise definition of a three-dimensional realization, I do have a precise definition of its dimension. The dimension has to do with chains of UIOs. So it proves that the DACO really is three-dimensional.

2:30 If you take that little diagram up there with the axioms on the axioms, and you look at the equations, where you have a reflection exactly the opposite, with two more arrows continuing to do a lot. In other words, have you tried to build some special circles? Oh, the special circles, yeah. See, the identity applies with all the non-identity elements. It's certainly a two-sided ideal. You can't multiply together two inputs and invent one, right? So therefore the non-ones form an ideal. That's a particular object, which you can think of as the hyper-surface, the hyper-boundary. So, if you, if you look at I prime, The I is the unique representable function. The I is the unit itself. These are the non-one elements. This is everything in I except the unit. That's actually the two sides of that, the right and the left. So if you take the push out, and you get something that should be called the dimension of the sphere. It's very interesting in the case of graphs. It's got a canonical point. In fact, it has only one point. Every point, every map from one, factors across I-prime. But the map from one is a constant, and one is not a constant. The constants are included in I-prime, although I-prime is generally a lot more important. So the sphere has only one point.

22:30 This is the screen that I'm going to run.