Constantin-Cosmin Todea
Technical University of Cluj-Napoca, Cluj-Napoca, Romania

A covariant functor from a small category $\mathcal{C}$ to the category of unital associative $k$-algebras ($k$ is a commutative ring with identity) is called a precosheaf of $k$-algebras. Category (convolution) algebras generalize group algebras and have been highlighted in the case of groupoid algebras notably in noncommutative geometry. Skew category algebras extend the concept of a skew group algebra to a precosheaf of $k$-algebras and, we show that we can view a skew category algebra as a unital subalgebra of some twisted tensor product. We also define and investigate induction of precosheaves of $k$-algebras by extending the work (in the group case) of Puig and Turull.