Dual Adjunctions Between Algebras and Coalgebras
نویسنده
چکیده
It is shown that the dual algebra functor from coalgebras to algebras has a left adjoint even if the base ring is not a field but an arbitrary commutative ring with 1. This result is proved as a corollary to a more general theorem on adjunctions between comonoids and monoids over suitable symmetric monoidal categories. MSC 2000: Primary 16B50, Secondary 18A40
منابع مشابه
Duality of Equations and Coequations via Contravariant Adjunctions
In this paper we show duality results between categories of equations and categories of coequations. These dualities are obtained as restrictions of dualities between categories of algebras and coalgebras, which arise by lifting contravariant adjunctions on the base categories. By extending this approach to (co)algebras for (co)monads, we retrieve the duality between equations and coequations f...
متن کاملCategories and all that - A Tutorial
This is a short introduction to categories with some emphasis on coalgebras. We start from introducing basic notions (categories, functors, natural transformations), move to Kleisli tripels and monads, with a short discussion of monads in Haskell, and continue with displaying the interplay between algebras, adjunctions and monads. Coalgebras are discussed and applied to the semantics of modal l...
متن کاملAdjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of Hom-tensor relations have been st...
متن کاملExemplaric Expressivity of Modal Logics
This paper investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains, and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution, and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The...
متن کاملConstraints, Adjunctions and (Co)algebras
The connection between constraints and universal algebra has been looked at in, and has given interesting results. Since the connection between universal algebra and category theory is so obvious, we will in this paper investigate if the usage of category theory has any impact on the results and/or reasoning and if anything can be gained from this approach. We construct categories of problem in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008