Fusion category algebras

Perfect Category-graded Algebras

In a perfect category every object has a minimal projective resolution. We give a sufficient condition for the category of modules over a category-graded algebra to be perfect. AMS Subject Classification (2000): 18E15, 16W50. In [6] the second author explored homological properties of algebras graded over a small category. Our interest in these algebras arose from our research on the homologica...

Semi-perfect Category-graded Algebras

We introduce the notion of algebras graded over a small category and give a criterion for such algebras to be semi-perfect. AMS Subject Classification (2000): 18E15,16W50.

On a category of cluster algebras

Abstract. We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and provide combinatorial methods for constructing special classes of monomorphisms and epimorphisms. In the case of cluster algebras from surfaces, we de...

On the category of pseudo-BCI-algebras

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.

Fusion frames in Hilbert modules over pro-C*-algebras