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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$ \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.

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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