Enriched indexed categories
Michael Shulman
TL;DR
This paper develops a comprehensive theory of categories that are both indexed over a base with finite products and enriched over an S-indexed monoidal category, unifying several existing categorical frameworks.
Contribution
It introduces a new framework for enriched indexed categories, generalizing classical, indexed, fibered, and internal categories, and describes their limits and free cocompletions.
Findings
Unified framework for enriched indexed categories
Defined limits and free cocompletions in this setting
Includes classical and internal categories as special cases
Abstract
We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V. This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases. We then describe the appropriate notion of "limit" for such enriched indexed categories, and show that they admit "free cocompletions" constructed as usual with a Yoneda embedding.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Logic, Reasoning, and Knowledge