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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• That term intro rule was probably all wrong (edit: thanks go to GuiGeek here). Also tried to consistently rename A => B, X => A.

• added below the very first definition at kernel a remark that spells out the universal property more explicitly. Also added mentioning of some basic examples.

• This is the list from proof assistant – Examples, and was (incompleteky) copied by hand into related entries, but we should make it (as done hereby) a standalone to be !includeed under “Related concepts” in relevant entries

All I did in editing was to group the proof assistants into “based on type/set theory” and “applicable to homotopy type theory”. Experts please hit “edit” and improve on it

• expanded chain homotopy: added the usual non-commuting diagram, a discussion of chain homotopy equivalence and slightly expanded the description in terms of left homotopy

• am starting something, but not done yet, nothing to be seen here for the moment

• a stub, just for completeness of the list of proof assistants

• A long time ago we had a discussion at graph about notions of morphism. I have written an article category of simple graphs which collects some properties of the category under one of those definitions (corresponding better, I think, to graph-theoretic practice).

• a stub, to satisfy links

• some bare minimum

• starting something – not done yet, but need to save

• added under “Selected writings” the articles cited elsewhere on the nLab

• a bare minimum, just to record the references

• Added a bunch of material to inverse semigroup under subsections of “Properties”.

• I just aadded a sentence about Yang-Mills theory to gauge group, but there are some aspects of that article I feel we might want to discuss:

I don’t think that the statement “gauge groups encoded redundancies” of the mathematical description of the physics is correct. One hears this every now and then, and I suppose the idea is the observation that physical observables have to be in the trivial representation of the gauge group, but there is more to the gauge group than that.

Notably Yang-Mills theory is a theory of connections on G-principal bundles. No mathematician would ever say that the group G in a G-principal bundle just encodes a redundancy of our descriptins of that bundle. And the reason is because it is true only locally: the thing is that $\mathbf{B}G = \{* \stackrel{g \in G}{\to} * \}$ has a single object and hence is connected , but it has higher homotopy groups, and that’s where all the important information encoded by the gauge group sits.

So I would say that instead of being a redundancy of the description, instead the gauge group of Yang-Mills theory enocedes precisely the homotopy type of its moduli space. This is rather important.

A different matter are global gauge symmetries such as those that the DHR-theory deals with.

• Page created, but author did not leave any comments.

• added to Yang-Mills instanton a discussion of instantons as tunnelings between Chern-Simons vacua.

• Page created, but author did not leave any comments.

• I noticed some inconsistencies in the section outline at algebraic theory, that must have come from different people editing different pieces and mixing up some global entry structure.

I have briefly tried to reinstantiate consistent order. But the entry could probably do with somebody looking over in its entirety with an editor-hat on.

• Added redirects and a description of other contributions.

• just a stub for the moment, in order to have a place for recording relevant references, such as

• Replaced Monoid_mult.png to LaTeX contents.