Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fixed points in representations of categories


Authors: J. Adámek and J. Reiterman
Journal: Trans. Amer. Math. Soc. 211 (1975), 239-247
MSC: Primary 18A30
MathSciNet review: 0376799
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Fixed points of endomorphisms of representations, i.e. functors into the category of sets, are investigated. A necessary and sufficient condition on a category K is given for each of its indecomposable representations to have the fixed point property. The condition appears to be the same as that found by Isbell and Mitchell for Colim: $ {\text{Ab}^K} \to {\text{Ab}}$ to be exact. A well-known theorem on mappings of Katětov and Kenyon is extended to transformations of functors.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 18A30

Retrieve articles in all journals with MSC: 18A30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0376799-X
PII: S 0002-9947(1975)0376799-X
Article copyright: © Copyright 1975 American Mathematical Society