Category of stereotype spaces

Abstract: In this talk I'll present some standard facts about the category $\operatorname{Ste}$ of stereotype spaces. These are locally convex spaces reflexive under the assumption that the dual space $X'$ is endowed with the topology of uniform convergence on totally bounded sets in $X$. It is known that this category is extremely wide, since it contains all quasicomplete barreled spaces (in particular, all Fréchet spaces). At the same time $\operatorname{Ste}$ is pre-abelian, bicomplete and a *-autonomous category. This, in a sense, makes $\operatorname{Ste}$ unique today among the categories of Functional Analysis in terms of its feature set and opens new unexpected connections between Functional Analysis and other areas of mathematics, such as Algebra and Geometry.

category theoryfunctional analysisrepresentation theory

Audience: learners

( paper | slides )

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Additive categories between algebra and functional analysis

Series comments: Aims & Scope: Exchange ideas and foster collaboration between researchers from representation theory and functional analysis working on categorical aspects of the theory. In addition to research talks, there will be four mini-courses of introductory character.

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