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Complex systems of systems (SoS) are characterized by multiple interconnectedsubsystems. Typically, each subsystem is designed and analyzed usingmethodologies and formalisms that are specific to the particular subsystemmodel of computation considered --- Petri nets, continuous time ODEs,nondeterministic automata, to name a few. When interconnecting subsystems, adesigner needs to choose, based on the specific subsystems models, a commonabstraction framework to analyze the composition. In this paper we introduce anew framework for abstraction, composition and analysis of SoS that builds onresults and methods developed in sheaf theory, category theory and topostheory. In particular, we will be modeling behaviors of systems using sheaves,leverage category theoretic methods to define wiring diagrams and formalizecomposition and, by establishing a connection with topos theory, define aformal (intuitionistic/constructive) logic with a sound sheaf semantics

Abstraction, Composition and Contracts: A Sheaf Theoretic Approach