994 research outputs found
A Universal Approach to Vertex Algebras
We characterize vertex algebras (in a suitable sense) as algebras over a
certain graded co-operad. We also discuss some examples and categorical
implications of this characterization.Comment: To appear in the Journal of Algebr
Automatic program generation from specifications using PROLOG
An automatic program generator which creates PROLOG programs from input/output specifications is described. The generator takes as input descriptions of the input and output data types, a set of transformations and the input/output relation. Abstract data types are used as models for data. They are defined as sets of terms satisfying a system of equations. The tests, the transformations and the input/output relation are also specified by equations
From Monomials to Words to graphs
Given a finite alphabet X and an ordering on the letters, the map \sigma
sends each monomial on X to the word that is the ordered product of the letter
powers in the monomial. Motivated by a question on Groebner bases, we
characterize ideals I in the free commutative monoid (in terms of a generating
set) such that the ideal generated by \sigma(I) in the free monoid
is finitely generated. Whether there exists an ordering such that
is finitely generated turns out to be NP-complete. The latter problem is
closely related to the recognition problem for comparability graphs.Comment: 27 pages, 2 postscript figures, uses gastex.st
Computads for generalised signatures
We introduce a notion of signature whose sorts form a direct category, and
study computads for such signatures. Algebras for such a signature are
presheaves with an interpretation of every function symbol of the signature,
and we describe how computads give rise to signatures. Generalising work of
Batanin, we show that computads with certain generator-preserving morphisms
form a presheaf category, and describe a forgetful functor from algebras to
computads. Algebras free on a computad turn out to be the cofibrant objects for
certain cofibrantly generated factorisation system, and the adjunction above
induces the universal cofibrant replacement, in the sense of Garner, for this
factorisation system. Finally, we conclude by explaining how many-sorted
structures, weak -categories, and algebraic semi-simplicial Kan
complexes are algebras of such signatures, and we propose a notion of weak
multiple category.Comment: 39 page
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