I gave *Seiberg-Witten theory* an Idea-paragraph, added the orinal reference and cross-linked with *N=2 D=4 super Yang-Mills theory* and with *electric-magnetic duality*.

started a minimum at *Anderson duality* just for compleness, see the other thread on *dualizing object in a closed category*.

added to *Isbell envelope* the three original reference posted by Richard Garner to the Category Theory mailing list today (or yesterday).

I don’t have time to look into this right now, I just copied those references there for the moment).

]]>I gave *Pontryagin duality for torsion abelian groups* its own entry, cross-linked of course with the examples-section at *Pontryagin dual* and with all other relevant entries.

Mainly I wanted to record this diagram here in a way that one could link to it quasi-directly:

$\array{ &\mathbb{Z}[p^{-1}]/\mathbb{Z} &\hookrightarrow& \mathbb{Q}/\mathbb{Z} &\hookrightarrow& \mathbb{R}/\mathbb{Z} \\ {}^{\mathllap{hom(-,\mathbb{R}/\mathbb{Z})}}\downarrow \\ &\mathbb{Z}_p &\leftarrow& \hat \mathbb{Z} &\leftarrow& \mathbb{Z} }$ ]]>added some actual text to *Verdier duality* (in the Idea-section). But it’s no really good yet. More later…

Section (with a flat) and projection (by an idempotent projector onto a subspace) of a polytope are duals of each other in the following sense: a section of the dual (polar body) of a polytope is the same as a projection of itself (say the primal) onto a subspace! Prove..

]]>All our entries which wanted to point to something like *dualizing module* (such as at *Verdier duality*) or the more general concept in a closed monoidal category (such as at *star-autonomous category*) used to point to the entry *dualizable object*, which however did not really discuss this specific concept of “dualizable object”.

Therefore I have now created *dualizing object in a closed category* and made these entries point to that, instead.

Mentioned that in homological algebra/stable homotopy theory one usually puts additional finiteness conditions on the would-be dualizing object and added a brief remark on *Anderson duality* as a fundamental example.

Added the recent reference on Langlands dual groups as T-dual groups to both *geometric Langlands correspondence* and *T-duality* together with a brief sentence. But nothing more as of yet.

I am constructing a table

*structure on algebras and their module categories - table*

and am including it into the relevant entries. This is a bit experimental for the moment. More details and variants should be added and maybe some of the relations stated in a better way. Help is appreciated.

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