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A duality between infinitary varieties and algebraic theories

Jiří Adámek, Václav Koubek, Jiří Velebil (2000)

Commentationes Mathematicae Universitatis Carolinae

A duality between λ -ary varieties and λ -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal λ , whenever λ -small products commute with 𝒟 -colimits in Set , then 𝒟 must be a λ -filtered category. We nevertheless introduce the concept of λ -sifted colimits so that morphisms between λ -ary varieties (defined to be λ -ary, regular right adjoints) are precisely the functors...

Adhesive and quasiadhesive categories

Stephen Lack, Paweł Sobociński (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.

Adhesive and quasiadhesive categories

Stephen Lack, Paweł Sobociński (2010)

RAIRO - Theoretical Informatics and Applications

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.

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