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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 4th 2013
• (edited Feb 4th 2013)

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.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 4th 2013

So far I have the following:

Tannaka duality for associative algebras

associative algebra category of modules
$A$ $Mod_A$
$R$-associative algebra $Mod_R$-2-module
sesquialgebra 2-ring = monoidal presentable category with colimit-preserving tensor product
bialgebra strict 2-ring: monoidal category with fiber functor
Hopf algebra rigid monoidal category with fiber functor
quasitriangular bialgebra braided monoidal category with fiber functor
triangular bialgebra symmetric monoidal category with fiber functor
quasitriangular Hopf algebra (quantum group) rigid braided monoidal category with fiber functor
triangular Hopf algebra rigid symmetric monoidal category with fiber functor