Stub to collect references.

]]>Added Yves Diers’ thesis.

]]>Added more links.

David White

]]>I hope this works. I’m trying to add a link.

David White

]]>transcendental extensions

Anonymouse

]]>algebraic element

Anonymouse

]]>transcendental elements

Anonymouse

]]>Mention that compact closed categories are self-dual.

]]>Thanks for the alert. Have cleared it now.

This is concerning, apparently the spammer managed to defeat the announcement mechanism for page creations.

]]>deleted spam

]]>Just a heads-up that this page is not doing what it is supposed to.

]]>In Dec 2018 (revision 72) I had spelled out in the entry the argument for the rheonomy principle from CDF91 III.3, noticing at the end that there is a gap in the argument, since the RHS of the differential equation III.3.29 (p. 653) depends on $d \theta^{\overline{\alpha}}$ not only through a contracted curvature, but also through a contracted vielbein field $\mu_{\overline{\alpha}}$.

Back then I had concluded with a paragraph indicating how this gap might be fixed.

But revisiting the story now, I don’t think this can be fixed, and I have now deleted my paragraph suggesting otherwise.

It looks to me like the concluding sentence below their (III.3.29) is wrong as stated, it forgets about the dependence on $\mu_{\overline{\alpha}}^B(x,0)$ evidently present in the line before, which is not given by the initial value data.

Nevertheless, I think the whole story works, one just has to be a little more careful.

Namely, applying the argument to the rheonomy of the vielbein fields, this term $\mu_{\overline{\alpha}}$ becomes the $d \theta^{\overline{\alpha}}$-leg of the spin-connection 1-form. Since this is an auxiliary field anyways it makes sense to grant that this term *is* actually known as initial data (“auxiliary initial data”). In particular, it should make sense to ask that the spin-connection actually vanishes along the odd directions.

Moreover, when applying the argument to the flux forms, $\mu_{\overline{\alpha}}$ happens to not appear, so that there is no issue in this case.

]]>Added Joshua Wrigley’s thesis.

]]>Added requirement of polynomials being non-zero, since every number is a root of the zero polynomial

Anonymouse

]]>Very confusing as written right now.

omer bojan

]]>acyclic types

Anonymouse

]]>Re #6: The quoted text looks correct. The sentence after the quote seems to have the roles of objects and morphisms mixed up.

]]>umm

An object $U$ in a category $C$ is

subterminalorpreterminalif any two morphisms with target $U$ and the same source are equal. In other words, $U$ is subterminal if for any object $X$, there is at most one morphism $X\to U$.If C has a terminal object 1, then U is subterminal precisely if the unique morphism U→1 is monic, so that U represents a subobject of 1; hence the name “sub-terminal.”

like anything associated with limits while the objects are unique the morphisms from or to them are not equal or unique but only unique up to isomorphism,

]]>Fixed the wording in the remark on adjointability of tensoring with an object not implying the dualizability of that object (here).

]]>Another rewording of the product condition

]]>transcendental numbers

Anonymouse

]]>I was just making an (IMO) minimal adjustment to the existing language. I don’t really know what precisely the original wording wanted to emphasize. I just wanted to reword it to forestall any reactions wondering about $U \times U$ not existing that might slow a reader down.

]]>Why not just say that the cone $U \leftarrow U \rightarrow U$ given by identities is a product?

]]>Changed the wording of an equivalent statement, so that it doesn’t leave open the possibility of a subterminal object $U$ for which $U \times U$ doesn’t exist.

]]>