Categories of integrable $sl(\infty)$, $o(\infty)$, $sp(\infty)$ - modules

In this talk we discuss two categories of integrable modules: modules with finite-dimensional weight spaces, and tensor modules. The latter modules form an interesting category on which the functor of algebraic dualization preserves the property of a module to have finite Loewy length. This is an unusual situation. Both categories are natural analogs of the category of finite-dimensional modules.