  Mereology is the study of parts and the relationships that hold between them.
We introduce a behavioral approach to mereology, in which systems and their
parts are known only by the types of behavior they can exhibit. Our discussion
is formally topos-theoretic, and agnostic to the topos, providing maximal
generality; however, by using only its internal logic we can hide the details
and readers may assume a completely elementary set-theoretic discussion. We
consider the relationship between various parts of a whole in terms of how
behavioral constraints are passed between them, and give an inter-modal logic
that generalizes the usual alethic modalities in the setting of symmetric
accessibility.

Logic;Category Theory