  A representation of $\mathfrak{gl}(V)=V \otimes V^*$ is a linear map $\mu
\colon \mathfrak{gl}(V) \otimes M \to M$ satisfying a certain identity. By
currying, giving a linear map $\mu$ is equivalent to giving a linear map $a
\colon V \otimes M \to V \otimes M$, and one can translate the condition for
$\mu$ to be a representation to a condition on $a$. This alternate formulation
does not use the dual of $V$, and makes sense for any object $V$ in a tensor
category $\mathcal{C}$. We call such objects representations of the curried
general linear algebra on $V$. The currying process can be carried out for many
algebras built out of a vector space and its dual, and we examine several cases
in detail. We show that many well-known combinatorial categories are equivalent
to the curried forms of familiar Lie algebras in the tensor category of linear
species; for example, the titular Brauer category "is" the curried form of the
symplectic Lie algebra. This perspective puts these categories in a new light,
has some technical applications, and suggests new directions to explore.
