kan A package for Induced Category Actions
نویسندگان
چکیده
The kan package was originally implemented in 1997 using the GAP 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor. This reduced version only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups. Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at [email protected].
منابع مشابه
2 3 Ju n 19 99 Using Automata to obtain Regular Expressions for Induced Actions ∗
Presentations of Kan extensions of category actions provide a natural framework for expressing induced actions, and therefore a range of different combinatorial problems. Rewrite systems for Kan extensions have been defined and a variation on the Knuth-Bendix completion procedure can be used to complete them – when possible. Regular languages and automata are a useful way of expressing sets and...
متن کاملGröbner Basis Techniques for Computing Actions of K - Categories ∗
This paper involves categories and computer science. Gröbner basis theory is a branch of computer algebra which has been usefully applied to a wide range of problems. Kan extensions are a key concept of category theory capable of expressing most algebraic structures. The paper combines the two, using Gröbner basis techniques to compute certain kinds of Kan extension.
متن کاملUsing Rewriting Systems to Compute Left Kan Extensions and Induced Actions of Categories
The aim is to apply string-rewriting methods to compute left Kan extensions, or, equivalently, induced actions of monoids, categories, groups or groupoids. This allows rewriting methods to be applied to a greater range of situations and examples than before. The data for the rewriting is called a Kan extension presentation. The paper has its origins in earlier work by Carmody and Walters who ga...
متن کاملDiagonal Fibrations Are Pointwise Fibrations
On the category of bisimplicial sets there are different Quillen closed model structures associated to various definitions of fibrations. In one of them, which is due to Bousfield and Kan and that consists of seeing a bisimplicial set as a simplicial object in the category of simplicial sets, fibrations are those bisimplicial set maps such that each of the induced simplicial set maps is a Kan f...
متن کاملThe category of monoid actions in Cpo
In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from...
متن کامل