Equivalences of comodule categories for coalgebras over rings
نویسندگان
چکیده
منابع مشابه
Semiperfect coalgebras over rings
Our investigation of coalgebras over commutative rings R is based on the close relationship between comodules over a coalgebra C and modules over the dual algebra C∗. If C is projective as an R-module the category of right C-comodules can be identified with the category σ[C∗C] of left C∗-modules which are subgenerated by C. In this context semiperfect coalgebras are described by results from mo...
متن کاملSymmetry for Comodule Categories
For coalgebras C over a field, we study when the categories CM of left C-comodules and MC of right C-comodules are symmetric categories, in the sense that there is a duality between the categories of finitely presented unitary left R-modules and finitely presented unitary left L-modules, where R and L are the functor rings associated to the finitely accessible categories CM and MC .
متن کاملModel-categories of Coalgebras over Operads
This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are deriv...
متن کاملDual coalgebras of algebras over commutative rings
In the study of algebraic groups the representative functions related to monoid algebras over fields provide an important tool which also yields the finite dual coalgebra of any algebra over a field. The purpose of this note is to transfer this basic construction to monoid algebras over commutative rings R. As an application we obtain a bialgebra (Hopf algebra) structure on the finite dual of t...
متن کاملBehavioural equivalences for coalgebras with unobservable moves
We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on special order enriched categories, i.e. categories whose homsets are endowed with suitable complete orders. Using this structure we provide an abstract notion of saturation, which allows us to define various (weak) be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2002
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00013-0