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INDUCTIVE AND PROJECTIVE LIMITS OF COVERING k-GROUPS OF n-GROUPS

INDUCTIVE AND PROJECTIVE LIMITS OF COVERING k-GROUPS OF n-GROUPS DEMONSTRATIO MATHHMATICAXV'.;No Ilf84Jacek MichalskiINDUCTIVE AND PROJECTIVE LIMITSOF COVERING k-GROUPS OF n-GROUPS1. IntroductionThis paper i s a continuation of the description of thetfcategory Covn of covering k-groups of n-groups. The notionof the category Cov£ has been introduced i n [6], where alsovarious c l a s s e s of morhpisms i n Cov£ have been described.In t h i s paper, which i s closely related to [6] , we giveconlrstructions of inductive and projective l i m i t s i n Covn and wedefine a pair of adjoint functors r and A as w e l l . Basingon properties of these functors we show that the categoryGrn+^ of (n+1)-groups i s a f u l l r e f l e c t i v e subcategory ofCovn+1 ( w i i e r e n = s*k).The terminology of our paper i s the same as that of [5] ,[6] ( c f . also [2], [3], [4]) where we also discuss?" relevantnotions. In those papers we always assume that n = sk, s = mq(admitting s = 1 and n = 1), where m, q may be indexed.k+1We r e c a l l http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

INDUCTIVE AND PROJECTIVE LIMITS OF COVERING k-GROUPS OF n-GROUPS

Michalski, Jacek
Demonstratio Mathematica , Volume 17 (1): 10 – Jan 1, 1984
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References (4)

Publisher
de Gruyter
Copyright
© by Jacek Michalski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1984-0106
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHHMATICAXV'.;No Ilf84Jacek MichalskiINDUCTIVE AND PROJECTIVE LIMITSOF COVERING k-GROUPS OF n-GROUPS1. IntroductionThis paper i s a continuation of the description of thetfcategory Covn of covering k-groups of n-groups. The notionof the category Cov£ has been introduced i n [6], where alsovarious c l a s s e s of morhpisms i n Cov£ have been described.In t h i s paper, which i s closely related to [6] , we giveconlrstructions of inductive and projective l i m i t s i n Covn and wedefine a pair of adjoint functors r and A as w e l l . Basingon properties of these functors we show that the categoryGrn+^ of (n+1)-groups i s a f u l l r e f l e c t i v e subcategory ofCovn+1 ( w i i e r e n = s*k).The terminology of our paper i s the same as that of [5] ,[6] ( c f . also [2], [3], [4]) where we also discuss?" relevantnotions. In those papers we always assume that n = sk, s = mq(admitting s = 1 and n = 1), where m, q may be indexed.k+1We r e c a l l

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 1984

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