  A modeloid, a certain set of partial bijections, emerges from the idea to
abstract from a structure to the set of its partial automorphisms. It comes
with an operation, called the derivative, which is inspired by
Ehrenfeucht-Fra\"iss\'e games. In this paper we develop a generalization of a
modeloid first to an inverse semigroup and then to an inverse category using an
axiomatic approach to category theory. We then show that this formulation
enables a purely algebraic view on Ehrenfeucht-Fra\"iss\'e games.
