Frobenius algebras appear in many parts of maths and have nice properties.  One can define algebra objects in any monoidal category, and there is a standard definition of when such an algebra object is Frobenius.  However, this definition is quite restrictive, and it is not satisfied by an algebra object of interest, related to the preprojective algebra, in the Temperley-Lieb category at a root of unity.  We will explore a more general definition of a Frobenius algebra object which covers this example, and will explore some of its properties.  This is joint work with Mathew Pugh.

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