A functor-valued invariant of tangles.
There is a classical result known as Baer’s Lemma that states that an -module is injective if it is injective for . This means that if a map from a submodule of , that is, from a left ideal of to can always be extended to , then a map to from a submodule of any -module can be extended to ; in other words, is injective. In this paper, we generalize this result to the category consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
This paper presents a generalized minimal realization theory of machines in a category which contains the Kleiski case. The minimal realization is the cheapest realization for a given cost functor. The final reachable realization of Arbib and Manes ([5]) and the minimal state approach for nondeterministic machines are included here.