Done.

]]>Hm, I forget why I put in that qualifiers. Let’s remove it.

]]>The table lists affine schemes as a (edit:) subcategory of finitely generated commutative algebras.

The category of affine schemes is antiequivalent to the category of all commutative rings. One can work over some ground ring $k$ if wanted, but finite generation is not needed for anything unless it is required at both sides. Some people consider just “affine algebras” over some $k$, but usually when talking the case of varieties.

However, spectrum can also be understood as a right adjoint to the global sections functor on the category of locally affine ringed spaces.

I do not know what the author meant with putting these finiteness requirements in the table.

]]>I have changed the table header from “Isbell duality” to “duality between algebra and geometry”. The former was meant to be read as a synonym for the latter, but I can see how that’s too ideosyncratic not to be confusing (as per the discussion here).

For the moment the page title (which is not displayed in the pages where this table is `!include`

-ed) remains the same. Because I am unsure if the software would correctly handle `!redirect`

s inside `!include`

s, and since I don’t have the time now to search for and change all the `!include`

-commands to this table.

I’m just seeing “Unknown node type: a” in Chrome.

]]>In revision 12 from October 2020, an anonymous edit tried to hyperlink the words “Gelfand-Kolmogorov”, but failed. I have fixed this now.

Of course the issue is that the hyperlinks are inside a `\text`

-environment inside a maths environment, and so necessarlily (?) Instiki syntax doesn’t work here – but HTML still does…

… or at least it does with Firefox. I suppose most other browsers show just broken links on this page here?

]]>added pointer to the equivalence between fully faithfulness of affine schemes in opposites of rings.

Undecided now whether to display mostly full inclusions or the equivalences onto their essential image. Table may deserve further reworking..

]]>added one more line to the table (super $L_\infty$-algebras $\leftrightarrow$ differential graded-commutative superalgebras)

]]>the table didn’t have the basic examples, such as *Gelfand duality* and *Milnor’s exercise*. Added now.