Notes on Coalgebras, Cofibrations and Concurrency

نویسندگان

  • Alexander Kurz
  • Dirk Pattinson
چکیده

We consider categories of coalgebras as (co)-fibred over a base category of parameters and analyse categorical constructions in the total category of deterministic and non-deterministic coalgebras.

برای دانلود 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

Coalgebras and Modal Logic for Parameterised Endofunctor

We study categories of coalgebras for endofunctors, which additionally depend on a parameter category. The corresponding category of coalgebras then naturally appears as cofibred over the parameters. We give examples of constructions in the cofibred framework and study the overall structure of such cofibrations. Moreover, the dependency of (modal) logics for coalgebras on a parameter category i...

متن کامل

Algebraic model structures

We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove “algebraic” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense underlies a cofibrantly generated algebraic mo...

متن کامل

The University of Chicago Algebraic Model Structures a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy

In Part I of this thesis, we introduce algebraic model structures, a new context for homotopy theory in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads and prove “algebraic” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense un...

متن کامل

The Microcosm Principle and Concurrency in Coalgebra

Coalgebras are categorical presentations of state-based systems. In investigating parallel composition of coalgebras (realizing concurrency), we observe that the same algebraic theory is interpreted in two different domains in a nested manner, namely: in the category of coalgebras, and in the final coalgebra as an object in it. This phenomenon is what Baez and Dolan have called the microcosm pr...

متن کامل

Computable Functions on Final Coalgebras

This paper tackles computability issues on final coalgebras and tries to shed light on the following two questions: First, which functions on final coalgebras are computable? Second, which formal system allows us to define all computable functions on final coalgebras? In particular, we give a definition of computability on final coalgebras, deriving from the theory of effective domains. We then...

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

برای دانلود 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

عنوان ژورنال:
  • Electr. Notes Theor. Comput. Sci.

دوره 33  شماره 

صفحات  -

تاریخ انتشار 2000