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Grothendieck Inclusion Systems

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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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Authors and Affiliations

  1. Institute of Mathematics “Simion Stoilow”, Romanian Academy, 21, Calea Grivitei St., 010702, Bucharest, Sector 1, Romania

    Răzvan Diaconescu

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  1. Răzvan Diaconescu
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Correspondence to Răzvan Diaconescu.

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Diaconescu, R. Grothendieck Inclusion Systems. Appl Categor Struct 19, 783–802 (2011). https://doi.org/10.1007/s10485-009-9211-6

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