$\mathfrak {F}$-projective objects
Author:
C. E. Hall
Journal:
Proc. Amer. Math. Soc. 26 (1970), 193-195
MSC:
Primary 18.10; Secondary 22.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0258910-5
MathSciNet review:
0258910
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Abstract | References | Similar Articles | Additional Information
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.
- C. E. Hall, Projective topological groups, Proc. Amer. Math. Soc. 18 (1967), 425–431. MR 212119, DOI https://doi.org/10.1090/S0002-9939-1967-0212119-X
- Karl Heinrich Hofmann, Zerfällung topologischer Gruppen, Math. Z. 84 (1964), 16–37 (German). MR 165030, DOI https://doi.org/10.1007/BF01112206
- Daniel M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294–329. MR 131451, DOI https://doi.org/10.1090/S0002-9947-1958-0131451-0
- A. Markoff, On free topological groups, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 9 (1945), 3–64 (Russian, with English summary). MR 0012301
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Additional Information
Keywords:
<!– MATH $\mathfrak {F}$ –> <IMG WIDTH="18" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\mathfrak {F}$">-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