Nested Sketches
نویسنده
چکیده
Since the fundamental work of Lawvere in 1963 [7] it is common to understand a theory as category with additional structure, to understand a model of the theory as a functor preserving the additional structure, and to represent homomorphisms by natural transformations. The resulting model category becomes a suitable subcategory of a functor category. Many different classes of mathematical structures have been described and investigated in this way. The aim of this paper is, to find a functorial model theory for those classes of algebras that appear naturally as semantics of algebraic specifications of parameterized data types, using initial respectively more general free functor semantics, and to extend the functorial model theory to specifications that use as well inductively defined data types as coinductively defined patterns of behavior and their systematic combinations.
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