Quasivarieties and varieties of ordered algebras: regularity and exactness
نویسندگان
چکیده
We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets. We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, in the enriched sense).
منابع مشابه
Minimal Varieties and Quasivarieties of Semilattices with One Automorphism
We describe all minimal quasivarieties and all minimal varieties of semilattices with one automorphism (considered as algebras with one binary and two unary operations).
متن کاملOn Finitely Based Groups and Nonfinitely Based Quasivarieties
We define the notion of strictly finitely based varieties of groups, and determine which finite groups are strictly finitely based. Then we use this result to prove the existence of ‘very nonfinitely based’ finite algebras, thereby solving two open problems in the theory of quasivarieties.
متن کاملKeith A . Kearnes Quasivarieties of Modules Over Path Algebras of Quivers Dedicated to the memory of Willem Johannes Blok
Let FΓ be a finite dimensional path algebra of a quiver Γ over a field F. Let L and R denote the varieties of all left and right FΓ-modules respectively. We prove the equivalence of the following statements. • The subvariety lattice of L is a sublattice of the subquasivariety lattice of L. • The subquasivariety lattice of R is distributive. • Γ is an ordered forest.
متن کاملThe Number of Proper Minimal Quasivarieties of Groupoids
It is shown that if an algebra has more than one element, is freely generated in some variety by one element and has a cancellative endomorphism semigroup then it generates a minimal quasivariety. This is used to construct uncountably many minimal quasivarieties of groupoids that are not varieties. A quasivariety [l] JÍ of algebras will be called implicationally complete or minimal if K has exa...
متن کاملProduct preservation and stable units for reflections into idempotent subvarieties
We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 27 شماره
صفحات -
تاریخ انتشار 2017