A Remark on Fixed Points of Functors in Topological Categories

Jiří Adámek
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Jiří Adámek: Technical University of Braunschweig

A chapter in Categorical Topology, 1996, pp 121-126 from Springer

Abstract: Abstract For a topological category $$\mathcal{K}$$ Set we prove that if a functor T $$\mathcal{K} \to {\mkern 1mu} {\text{ }}\mathcal{K}$$ has a fixed cardinal α (i.e. for each object K with card (UK) = α we have card (UTK) ⩽ α) the T has a least fixed point and if T has a successive pair of fixed cardinal α and α+, then T has a greatest fixed point. This extends results of Adá and Koubek.

Keywords: fixed point of a functor; topological category; 18A99; 68Q65 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_11

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DOI: 10.1007/978-94-009-0263-3_11

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