  The introduction of the categorical notion of closure operators has unified
various important notions and has led to interesting examples and applications
in diverse areas of mathematics (see for example, Dikranjan and Tholen
(\cite{DT})). For a topological space it is well-known that the associated
closure and interior operators provide equivalent descriptions of the topology,
but this is not true in general. So, it makes sense to define and study the
notion of interior operators $I$ in the context of a category $\mathfrak C$ and
a fixed class $\mathcal M$ of monomorphisms in $\mathfrak C$ closed under
composition in such a way that $\mathfrak C$ is finitely $\mathcal M$-complete
and the inverse images of morphisms have both left and right adjoint, which is
the purpose of this paper.
