Some Categorical Algebraic Properties: Counter-Examples for Functor Categories |
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Authors: | Email author" target="_blank">Dali?ZangurashviliEmail author |
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Institution: | (1) Laboratory of Synergetics, Georgian Technical University, 77 Kostava Str., 0175, Tbilisi, Georgia and A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, 1 Aleksidze Str., 0193 Tbilisi, Georgia |
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Abstract: | This work is a complement to the author s earlier papers, where it is shown that a functor category
inherits from
such properties as amalgamation, transferability and congruence extension if
has either products or certain pushouts. A general scheme is given for constructing counter-examples which show that the latter condition on
is essential. In particular, it is shown that the functor categories
,
,
(
resp.) do not satisfy the amalgamation (congruence extension resp.) property in general. Moreover, one class of categories is described, where the condition of the existence of certain pushouts is not only sufficient, but also necessary for
to preserve the considered properties of
.Mathematics Subject Classifications (2000) 18A25, 18A32, 18B99, 08B26.Dali Zangurashvili: The support rendered by INTAS Grant 97 31961 is gratefully acknowledged. |
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Keywords: | amalgamation transferability congruence extension properties functor category cogenerating set finite group integral domain field metric space |
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