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Graphbased logic and sketches I: The general framework. Available by web browser from http://www.cwru.edu/1/class/mans/math/pub/wells
, 1996
"... Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic. ..."
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Cited by 8 (4 self)
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Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic.
How Algebraic Is Algebra?
, 2001
"... . The 2category VAR of finitary varieties is not varietal over CAT . We introduce the concept of an algebraically exact category and prove that the 2category ALG of all algebraically exact categories is an equational hull of VAR w.r.t. all operations with rank. Every algebraically exact category ..."
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Cited by 1 (0 self)
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. The 2category VAR of finitary varieties is not varietal over CAT . We introduce the concept of an algebraically exact category and prove that the 2category ALG of all algebraically exact categories is an equational hull of VAR w.r.t. all operations with rank. Every algebraically exact category K is complete, exact, and has filtered colimits which (a) commute with finite limits and (b) distribute over products; besides (c) regular epimorphisms in K are productstable. It is not known whether (a)  (c) characterize algebraic exactness. An equational hull of VAR w.r.t. all operations is also discussed. 1.
Modular Specifications: Constructions With Finite Colimits, Diagrams, Isomorphisms
, 1996
"... : The composition of modular specifications can be modeled, in a category theoretic framework, by colimits of diagrams. Pushouts in particular describe the combination of two specifications sharing a common part. This work extends this classic idea along three lines. First, we define a term language ..."
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: The composition of modular specifications can be modeled, in a category theoretic framework, by colimits of diagrams. Pushouts in particular describe the combination of two specifications sharing a common part. This work extends this classic idea along three lines. First, we define a term language to represent modular specifications built with colimit constructions over a category of base specifications. This language is formally characterized by a finitely cocomplete category. Then, we propose to associate with each term a diagram. This interpretation provides us with a more abstract representation of modular specifications because irrelevant steps of the construction are eliminated. We define a category of diagrams, which is a completion of the base category with finite colimits. We prove that the interpretation of terms as diagrams defines an equivalence between the corresponding categories, which shows the correctness of this interpretation. At last, we propose an algorithm to no...