Title: Tensor Algebras in Tensor Categories

Abstract: This talk explores the standard construction of tensor algebras. Starting with a bimodule (M) over an algebra (A), one can form the tensor algebra (T_A(M)) consisting of all finite tensors of elements from M with multiplication given by the tensor product over A. In addition, we will discuss tensor categories which generalize the notion of tensor product of vector spaces to more abstract settings. Finally, we will take a closer look at how the construction of tensor algebras can be generalized to this abstract setting of tensor categories and how it relates to my current research.