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Turkish Journal of Mathematics

Author ORCID Identifier

MEHMET AKİF ERDAL: 0000-0003-4380-9013

DOI

10.55730/1300-0098.3566

Abstract

We study fibration category structures induced by enrichments over symmetric monoidal categories that are also fibration categories. Let $\mathcal V$ be a monoidal category that is also a fibration category. Assume that $\mathcal V$ has an interval object. We show that the fibration category structure on $\mathcal V$ can be transferred over any $\mathcal V$-enriched category through corepresentable functors provided that certain power objects exists. We also give its $G$-equivariant extension for a group $G$, so that under mild conditions the category of $G$-objects in a $\mathcal V$-enriched category admits a (non-trivial) fibration category structure. We later show that several categories of topological algebras and associative algebras, and their $G$-equivariant analogues, can be made into fibration categories obtained in this way. We also present some applications of our results by recovering some existing results on (equivariant) $K$ and $E$-theories of operator algebras.

Keywords

Fibration category, homotopy, enriched category, path object, equivariant homotopy

First Page

1138

Last Page

1155

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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