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$ \mathfrak{F}$-projective objects

Author: C. E. Hall
Journal: Proc. Amer. Math. Soc. 26 (1970), 193-195
MSC: Primary 18.10; Secondary 22.00
MathSciNet review: 0258910
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Abstract: Previously, projective abelian topological groups were defined based upon the requirement that free abelian topological groups be projective. In the present paper it is observed that a similar definition of projective relative to a functor which has a right adjoint leads to equivalent results in a much more general setting. These results are then specialized to the category of topological groups (with Markov's free functor) for a detailed example.

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

  • [1] C. Hall, Projective topological groups, Proc. Amer. Math. Soc. 18 (1967), 425-431. MR 35 #2994. MR 0212119 (35:2994)
  • [2] K. Hofmann, Zerfällung Topologischer Gruppen, Math. Z. 84 (1964), 16-37. MR 29 #2321. MR 0165030 (29:2321)
  • [3] D. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329. MR 24 #A1301. MR 0131451 (24:A1301)
  • [4] A. Markov, On free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 3-64; English transl., Amer. Math. Soc. Transl. (1) 8 (1962), 195-272. MR 7, 7. MR 0012301 (7:7b)

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Keywords: $ \mathfrak{F}$-projective, adjoint functor, retract, completely regular space, free topological group, free functor, projective, Stone-Čech compactification, polynomial ring
Article copyright: © Copyright 1970 American Mathematical Society

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