Descent in categories of (co)algebras
نویسندگان
چکیده
منابع مشابه
On descent for coalgebras and type transformations
We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...
متن کاملDistributivity of categories of coalgebras
We prove that for any Set-endofunctor F the category SetF of F -coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever SetF has finite products.
متن کاملCotensor Coalgebras in Monoidal Categories
We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.
متن کاملFinal coalgebras in accessible categories
We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p...
متن کاملLimits in Categories of Vietoris Coalgebras
Motivated by the need to reason about the behaviour of hybrid systems, which is both discrete and continuous, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one — intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor has a final coalgebra if it respects certain con...
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: Homology, Homotopy and Applications
سال: 2005
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2005.v7.n1.a1