5,040 research outputs found
Variations on Algebra: monadicity and generalisations of equational theories
Dedicated to Rod Burstal
Proto-exact categories of matroids, Hall algebras, and K-theory
This paper examines the category of pointed matroids
and strong maps from the point of view of Hall algebras. We show that
has the structure of a finitary proto-exact category -
a non-additive generalization of exact category due to Dyckerhoff-Kapranov. We
define the algebraic K-theory of
via the Waldhausen construction, and show that it is
non-trivial, by exhibiting injections from the stable homotopy groups of spheres for
all . Finally, we show that the Hall algebra of is
a Hopf algebra dual to Schmitt's matroid-minor Hopf algebra.Comment: 29 page
Towards a Convenient Category of Topological Domains
We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models
A Convenient Category of Domains
We motivate and define a category of "topological domains",
whose objects are certain topological spaces, generalising
the usual -continuous dcppos of domain theory.
Our category supports all the standard constructions of domain theory,
including the solution of recursive domain equations. It also
supports the construction of free algebras for (in)equational
theories, provides a model of parametric polymorphism,
and can be used as the basis for a theory of computability.
This answers a question of Gordon Plotkin, who asked
whether it was possible to construct a category of domains
combining such properties
Cartesian closed 2-categories and permutation equivalence in higher-order rewriting
We propose a semantics for permutation equivalence in higher-order rewriting.
This semantics takes place in cartesian closed 2-categories, and is proved
sound and complete
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