2-Categorical aspects of strong shape |
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Authors: | Luciano Stramaccia |
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Institution: | Dipartimento di Matematica e Informatica, Universitá di Perugia, via Vanvitelli, I-06123 Perugia, Italy |
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Abstract: | For every pair (C,K) of groupoid enriched categories, we define two related categories S(C,K) and SS(C,K). In the case (C,K)=(TOP,ANR) they are isomorphic, respectively, to the classical shape category Sh(TOP) of Mardeši? and Segal and to the strong shape category of topological spaces SSh(1)(TOP) of height 1, defined by Lisicá and Mardeši?. Moreover, for (C,K)=(CM,ANR), where CM is the category of compact metric spaces, there is an isomorphism SSh(CM)≅SS(CM,ANR). A new characterization of topological strong shape equivalences is also given. |
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Keywords: | 18B40 55P55 55P65 54C56 18B30 18D20 54B30 |
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