Towards M-Adhesive Categories based on Coalgebras and Comma Categories

نویسنده

  • Julia Padberg
چکیده

In this contribution we investigate several extensions of the powerset that comprise arbitrarily nested subsets, and call them superpower set. This allows the definition of graphs with possibly infinitely nested nodes. additionally we define edges that are incident to edges. Since we use coalgebraic constructions we refer to these graphs as corecursive graphs. The superpower set functors are examined and then used for the definition of M-adhesive categories which are the basic categories forM-adhesive transformation systems. So, we additionally show that coalgebras SetsF are M-adhesive categories provided the functor F : Sets→ Sets preserves pullbacks along monomorphisms.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Chu I: Cofree Equivalences, Dualities and *-Autonomous Categories

Received We study three comonads derived from the comma construction. The induced coalgebras correspond to the three concepts displayed in the title of the paper. The comonad that yields the-autonomous categories is, in essence, the Chu construction, which has recently awaken much interest in computer science. We describe its couniversal property. It is right adjoint to the inclusion of-autonom...

متن کامل

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 کامل

Construction and Properties of Adhesive and Weak Adhesive High-Level Replacement Categories

As presented in Ehrig et al. (Fundamentals of Algebraic Graph Transformation, EATCS Monographs, Springer, 2006), adhesive high-level replacement (HLR) categories and systems are an adequate framework for several kinds of transformation systems based on the double pushout approach. Since (weak) adhesive HLR categories are closed under product, slice, coslice, comma and functor category construct...

متن کامل

Model-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 کامل

Colby]Fuller Duality between Coalgebras

w x In 8 , K. Morita introduced a useful notion of duality between categories of modules, usually called ‘‘Morita duality.’’ He proved that every duality is given by contravariant hom functors defined by a bimodule which is an injective cogenerator for both categories of modules. On the other hand, the equivalences between categories of comodules over a coalgebra w x were characterized by M. Ta...

متن کامل

ذخیره 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 2017