… Let 2 be the category 0~» 1, the totally ordered set of two elements. Then the functor category
& is the category whose objects are the morphisms of 6E … We have two evaluation functors …

… study of modules over a ring. The functor categories that we study most are (R —mod, Ab)
and (mod —R, Ab), the categories of additive functors from the category of finitely presented …

… , we introduce the notion of a modular functor with central charge, which can be … a modular
functor, namely the one coming from the Wess–Zumino–Witten model of conformal field theory…

… races: Tf T is right-continuous, right exact functor from 3 to oA … to the functor - 3) A , We
return to functor categories at the ernd of Chapter Three to prove that if a corplete category eț3 …

… a functor F : C → R-mod where R-mod is the category of R-modules. Such a representation
may be identified as a module for a certain algebra which we now introduce. We define the …

… Plainly it induces a lift in the ambient functor category, so we only need show that it satisfies
the conditions to induce left and right module maps. The former follows from the hypothesis …

… In particular Kan's work implies that adjoint functors exist for. functors on the category of
modules over a ring, the case in which we will wish to use it. The definition of relative adjoint is …

… We prove in fact that Ext:(-,a) provides a dualizing functor for the category of A-modules
of finite length. This fact, with A = Q, was implicit in our earlier discussion of Gorenstein rings. …

… CATEGORIES, DIAGRAMS AND FUNCTORS In this section we introduce some of the basic
language of category theory involving the notions of category and functor… of the set theory, …

… modules are discussed, for example we discuss when the category of entwined modules is a
monoidal category… We use entwining structures mainly as a tool to unify all kinds of modules…