somebody created *Freyd category*

starting a stand-alone Section-entry (to be `!include`

ed as a section into *D=11 supergravity* and into *D’Auria-Fré formulation of supergravity*)

So far it contains lead-in and statement of the result, in mild but suggestive paraphrase of CDF91, §III.8.5.

I am going to spell out at least parts of the proof, with some attention to the prefactors.

(Namely, various normalization conventions in CDF91 are a little unnatural. One needs to transform carefully to get the good form of the EOMs, notably the factor of 1/2 in $\mathrm{d} G_7 = \tfrac{1}{2} G_4 \, G_4$.)

]]>I have started an entry *Majorana spinor* with discussion of how the physicist’s concept going by that name is a *real structure* on a complex spin representation.

Initially I had wanted to just follow the note by Figueroa-O’Farrill, but either I am missing something or else there is a gap in the argument there.

So in particular at the moment I have just one direction “Majorana structure is real structure”, not the converse.

(And why is it that the proposition number cross referencing is again broken?)

]]>New page: double category of algebras.

]]>I am working on entries related to [[generalized complex geometry]]. My aim is to tell the story in the correct way as the theory of the *Lie 2-algebroid* called the

- [[standard Courant algebroid]]

Most, if not all, of the generalized complex geometry literature, uses the "naive" definition of Courant algebroids that regards them as vector bundles with some structure on them and is being vague to ignorant about what the right morphisms should be.

As discussed at [[Courant algebroid]] we know that we are really dealing with a Lie 2-algebroid and hence know where precisely this object lives. This provides some useful, I think, perspectives on some of the standard constructions. I want to eventually describe this. For the moment I have just the material at [[standard Courant algebroid]] with only two most basic observations (which, however, in my experience already take a nontrivial amount of time on the blackboard to explain to somebody used to the "naive" picture usually presented in the literature).

]]>added pointer to

- Kurt Lechner, Mario Tonin,
*World-manifold and target space anomalies in heterotic Green-Schwarz strings and five-branes*, in:*Gauge Theories, Applied Supersymmetry and Quantum Gravity II*, pp. 311-318 (1997) (arXiv:hep-th/9610110, doi:10.1142/9781848160927_0022)

Based on a private discussion with Mike Shulman, I have added some explanatory material to inductive type. This however should be checked. I have created an opening for someone to add a precise type-theoretic definition, or I may get to this myself if there are no takers soon.

]]>Copied some of Mike’s blog post to indexed monoidal category, having worked on Charles Peirce if you want to know why. It needs wikifying.

]]>crated [[D'Auria-Fre formulation of supergravity]]

there is a blog entry to go with this here

]]>Some $\times$ were written as $x$, so fixed. There were sign changes going on that I didn’t understand, $p_2 - (\frac{1}{2}p_2)^2$ and $p_2 + (\frac{1}{2}p_1)^2$.

]]>Stub to collect references.

]]>Explain the connection with enriched monads

]]>What purpose is this page intended to serve? At the moment it just links to category of fibrant objects. Is there a reason this is not merged with that page?

]]>added at *TC* some references on computing THH for cases like $ko$ and $tmf$, here

I've edited the [[About]] page a little. My initial intention was just to update the technical information but I ended up adding a load more, mainly to expand on the "lab book" view. Given that we've discussed this back-and-forth for quite some time, I felt it time someone started actually modifying the page itself. Of course, if you don't like what I've said then **change it**!

It *is* a wiki, after all - even if it isn't an encyclopaedia.

algebraically independent subsets

Anonymouse

]]>created *fibrant type* with an Idea-section

The page split coequalizer said that the canonical presentation of an Eilenberg–Moore algebra is a split coequalizer in the category of algebras. I don’t think that’s right – if I recall correctly it’s reflexive there, but in general not split until you forget down to the underlying category. So I changed the page.

]]>A number of examples and counterexamples have been firmed up at presentation axiom. Some of them devolve on an observation made by Jonas Frey a few days ago at internally projective object, for which I added a simple proof. There are still some points that needed to be clarified regarding the internalization of the presentation axiom, but for now the discussion is concentrated on relations between externally projeective and internally projective objects.

]]>A stub so far.

]]>transcendental extensions

Anonymouse

]]>Entry on lattice ordered groups. Work in progress.

]]>Partially ordered abelian groups whose partial order is a pseudolattice

Anonymous

]]>Page created, but author did not leave any comments.

Anonymous

]]>Creating the page. Described briefly both the usual Lack model structure and the model structure using semi-strict equivalences coming from my thesis. A lot more could be added.

]]>