On the external characterization of topological functors
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We characterize topological functors purely in terms of functors and natural transformations, free of any references to particular kinds of functor, such as faithful of full. This differs from the characterization given by Brümmer and Hoffmann (Lect. Notes in Math 540 (1976) 136–151). Using this characterization we give an external proof that a topological functor has a left and right adjoint. In addition we use the characterization to give a new external proof of Wyler's taut lifts theorem.
KeywordsNumber Theory Algebraic Geometry Topological Group Natural Transformation Topological Functor
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- Brümmer, G.C.L., Topological functors and structure functors. Proc. Conf. Mannheim 1975 on Categorical Topology. Lect. Notes in Math. 540, 109–135 (1976).Google Scholar
- Brümmer, G.C.L. and Hoffmann, R.E., An external characterization of Topological functors. Proc. Conf. Mannheim 1975 on Categorical Topology. Lect. Notes in Math. 540, 136–151 (1976).Google Scholar
- Brümmer, G.C.L. and Hoffmann, R.E., Remarks on topologicity of functors, Proc. S. Afr. Math. Soc.5, 83–85 (1975).Google Scholar
- Herrlich, H., Topological functors. General Topology and Appl.4 125–142 (1974).Google Scholar
- Herrlich, H., Initial completions, Math. Z.150, 101–110 (1976).Google Scholar
- Hušek, M. Construction of special functors and its applications. Comment. Math. Univ. Carolinae8, 555–566 (1967).Google Scholar
- MacLane, S. Categories for the working mathematician, Berlin-Heidelberg-New York: Springer-Verlag 1971.Google Scholar
- Wyler, O. On the categories of general topology and topological algebra. Arch. Math. (Basel)22, 7–17 (1971)Google Scholar