  This paper presents meta-logical investigations based on category theory
using the proof assistant Isabelle/HOL. We demonstrate the potential of a free
logic based shallow semantic embedding of category theory by providing a
formalization of the notion of elementary topoi. Additionally, we formalize
symmetrical monoidal closed categories expressing the denotational semantic
model of intuitionistic multiplicative linear logic. Next to these
meta-logical-investigations, we contribute to building an Isabelle category
theory library, with a focus on ease of use in the formalization beyond
category theory itself. This work paves the way for future formalizations based
on category theory and demonstrates the power of automated reasoning in
investigating meta-logical questions.
