Grothendieck Inclusion Systems (abstract)
Inclusion systems have been introduced in algebraic specification
theory as a categorical structure supporting the development of a
general abstract logic-independent approach to the algebra of
specification (or programming) modules. Here we extend the concept of
indexed categories and their Grothendieck flattenings to inclusion
systems. An important practical significance of the resulting
Grothendieck inclusion systems is that they allow the development of
module algebras for multi-logic heterogeneous specification
frameworks. At another level, we show that several inclusion systems
in use in some syntactic (signatures, deductive theories) or semantic
contexts (models) appear as Grothendieck inclusion systems too. We
also study several general properties of Grothendieck inclusion
systems.
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