Axiom Systems for Category Theory in Free Logic

This document provides a concise overview on the core results of our previous work on the exploration of axioms systems for category theory. Extending the previous studies (http://arxiv.org/abs/1609.01493) we include one further axiomatic theory in our experiments. This additional theory has been suggested by Mac Lane in 1948. We show that the axioms proposed by Mac Lane are equivalent to the ones we studied before, which includes an axioms set suggested by Scott in the 1970s and another axioms set proposed by Freyd and Scedrov in 1990, which we slightly modified to remedy a minor technical issue.