Generic partiality for 32\frac{3}{2}-institutions

$\frac{3}{2}$-institutions have been introduced as an extension of institution theory that accommodates implicitly partiality of the signature morphisms together with its syntactic and semantic effects. In this paper we show that ordinary institutions that are equipped with an inclusion system for their categories of signatures generate naturally $\frac{3}{2}$ -institutions with explicit partiality for their signature morphisms. This provides a general uniform way to build 3 -institutions for the foundations of conceptual blending and software evolution. Moreover our general construction allows for an uniform derivation of some useful technical properties.Comment: arXiv admin note: substantial text overlap with arXiv:1708.0967

3/2-Institutions: an institution theory for conceptual blending

We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other application domains are possible (such as software evolution). The particularity of this extension is a reliance on ordered-enriched categorical structures

Polyadic systems, representations and quantum groups

Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.Comment: 51 pages, 1 table, 1 figure, amsart. In this version: small changes. For concise (without commutative diagrams, quiver diagrams, table and figure) journal version, see http://www-nuclear.univer.kharkov.ua/lib/1017_3%2855%29_12_p28-59.pd