Algebraic exponentiation for Lie algebras

Abstract: It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal category. In this way, we add some new examples to the brief list of known locally algebraically cartesian closed categories, including the categories of Lie superalgebras and differentially graded Lie algebras amongst others.