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Description: |
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.
Area(s): Category Theory
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Date: |
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| Start Time: |
15.00 |
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Speaker: |
Jirí Adámek (University of Braunschweig)
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Place: |
5.5
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| Research Groups: |
-Algebra, Logic and Topology
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See more:
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<Main>
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