A Brief Introduction to Coalgebra Representation Theory
نویسنده
چکیده
In this survey, we review fundamental properties of coalgebras and their representation theory. Following J.A. Green we present the block theory of coalgebras using indecomposable injectives comodules. Using the cohom and cotensor functors we state Takeuchi-Morita equivalence and use it to sketch the proof of existence of “basic” coalgebras, due to the author and S. Montgomery. This leads to a discussion of theory of path coalgebras, quivers and representations. Some quantum and algebraic group examples are given.
منابع مشابه
Expressivity of finitary coalgebraic logics
We give a brief introduction to the theory of coalgebras and discuss the connection between coalgebra and modal logic. In the second more technical part of this paper summarizing known results we prove that the finitary version of Moss’ coalgebraic logic has the Hennessy-Milner property.
متن کاملAutomata and Coinduction (an Exercise in Coalgebra) Automata and Coinduction (an Exercise in Coalgebra)
The classical theory of deterministic automata is presented in terms of the notions of homomor-phism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the p...
متن کاملIntroduction to Coalgebra
A survey of parts of General Coalgebra is presented with applications to the theory of systems. Stress is laid on terminal coalgebras and coinduction as well as iterative algebras and iterative theories. 1. Preface: Is this Really an Introduction to Coalgebra? For my series of lectures on coalgebra on the preconference to CTCS 2002 I prepared a short text called “Introduction to Coalgebra” that...
متن کامل2 6 Se p 20 06 geometry and reducibility of induction of Hopf group co - algebra
In this work we study the induction (induced and coinduced)theory for Hopf group coalgebra. We define a substructure B of a Hopf group coalgebra H, called subHopf group coalgebra. Also, we have introduced the definition of Hopf group suboalgebra and group coisotropic quantum subgroup of H. The properties of the algebraic structure of the induced and coinduced are given. Moreover, a framework of...
متن کاملFixpoint Logics and Automata: A Coalgebraic Approach
A long and fertile tradition in theoretical computer science, going back to the work of Büchi and Rabin, links the field of (fixpoint) logic to that of automata theory. In particular, automata operating on potentially infinite structures such as streams, trees, graphs or transition systems, provide an invaluable tool for the specification and verification of the ongoing behavior of systems. An ...
متن کامل