Weak Relational Products

The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version, any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categorical properties of the new construction and prove several (weak) versions of propositions well-known for relational products.

[1]  John G. Sanderson.  Types and structures , 1980 .

[2]  Wolfram Kahl,et al.  A Study on Symmetric Quotients , 1998 .

[3]  Hans Zierer,et al.  Relation Algebraic Domain Constructions , 1991, Theor. Comput. Sci..

[4]  Roger D. Maddux.  The derivation of identities involving projection functions , 1993 .

[5]  Giuseppe Longo,et al.  Categories, types and structures - an introduction to category theory for the working computer scientist , 1991, Foundations of computing.

[6]  Jules Desharnais,et al.  Monomorphic Characterization of n-ary Direct Products , 1999, Inf. Sci..

[7]  Dany Serrato,et al.  Squares and rectangles in relation categories. Three cases: semilattice, distributive lattice and Boolean non-unitary , 1995 .

[8]  Gunther Schmidt,et al.  Comparing Two Different Approaches to Products in Abstract Relation Algebra , 1993, AMAST.

[9]  Gunther Schmidt,et al.  Relationen und Graphen , 1989, Mathematik für Informatiker.

[10]  Andre Scedrov,et al.  Categories, allegories , 1990, North-Holland mathematical library.

[11]  Gunther Schmidt,et al.  Relations and Graphs: Discrete Mathematics for Computer Scientists , 1993 .

[12]  Maurice Nivat,et al.  Algebraic Methodology and Software Technology (AMAST’93) , 1994, Workshops in Computing.

[13]  Michael Winter.  Strukturtheorie heterogener Relationenalgebren mit Anwendung auf Nichtdeterminismus in Programmiersprachen , 1998 .

[14]  Abraham Kandel,et al.  Discrete mathematics for computer scientists , 1983 .