Algebra, Logic and Topology

 

Latest News
The web page of CMUC moved to http://cmuc.mat.uc.pt

 
   

Members

Seminars

Events

Publications

 
 

details

Title
Terminal Coalgebras as Sets or Classes

Abstract
For endofunctors H of Set, coalgebras represent dynamical systems of the type expressed by H, and a terminal coalgebra T represents the collection of all possible behaviours of states of such systems. This collection can be a class: not every set functor has a terminal coalgebra, but every endofunctor of the category of classes has one. And every set functor has an essentially unique extension to the category of classes. Example: the power-set functor P extends to the functor P' assigning to every class X the class P'X of all (small) subsets of X . A terminal coalgebra is the algebra of all rooted, non-ordered trees modulo the greatest bisimulation. The above result sharpens the Final Coalgebra Theorem of Aczel and Mendler: they proved that every set-based endofunctor has a terminal coalgebra. We now prove that all endofunctors are set-based.

Areas of interest
Category Theory

Speaker(s)
Jirí Adámek (University of Braunschweig)

Date
October 13, 2003

Time
15.00

Room
5.5

 
     
 

CMUC
Apartado 3008,
3001 - 454 Coimbra, Portugal
T:+351 239 791 150
F:+351 239 793 069
cmuc@mat.uc.pt
-
developed by Flor de Utopia