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and Concrete Categories The Joy of Cats Dedicated to Bernhard Banaschewski The newest edition of the file of the present book can be downloaded from http://katmat.math.uni-bremen.de/acc The authors are grateful for any improvements, corrections, and remarks, and can be reached at the addresses Jǐŕı Adámek, email: adamek@iti.cs.tu-bs.de Horst Herrlich,… (More)

- Peter Aczel, Jirí Adámek, Stefan Milius, Jiri Velebil
- Theor. Comput. Sci.
- 2003

In#nite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has #nal coalgebras for all functors H ( ) + X , then those coalgebras, TX… (More)

- Jirí Adámek, Václav Koubek
- Theor. Comput. Sci.
- 1995

- Jirí Adámek
- 2005

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… (More)

- Jirí Adámek, Frantisek Plasil
- Journal of Software Maintenance
- 2005

We discuss the problem of defining a composition operator in behavior protocols in a way which would reflect false communication of the software components being composed. Here the issue is that the classical way in the ADLs supporting behavior description, such as Wright and TRACTA, is to employ a CSP-like parallel composition which inherently yields only… (More)

- Jirí Adámek, Filippo Bonchi, Mathias Hülsbusch, Barbara König, Stefan Milius, Alexandra Silva
- FoSSaCS
- 2012

Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this paper, we use the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and… (More)

- Jirí Adámek, Dominik Lücke, Stefan Milius
- ITA
- 2007

For finitary set functors preserving inverse images several concepts of coalgebras A are proved to be equivalent: (i) A has a homomorphism into the initial algebra, (ii) A is recursive, i.e., A has a unique coalgebra-to-algebra morphism into any algebra, and (iii) A is parametrically recursive. And all these properties mean that the system described by A… (More)

- Jirí Adámek
- Theor. Comput. Sci.
- 2003

Continuous endofunctors F of locally nitely presentable categories carry a natural metric on their nal coalgebra. Whenever F(0) has an element, this metric is proved to be a Cauchy completion of the initial algebra of F . This is illustrated on the poset of real numbers represented as a nal coalgebra of an endofunctor of Pos by Pavlovi% c and Pratt. Under… (More)

- Jirí Adámek
- J. Log. Comput.
- 2002

For -continuous endofunctors of Set an ordering of a final coalgebra is exhibited which makes a CPO. Moreover, an initial algebra, considered as a canonical subobject of , has as its ideal completion. In more generality, for -continuous endofunctors of locally finitely presentable categories the analogous result holds: here the ordering is considered on the… (More)

- Jirí Adámek
- 1991