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7 - Multicategorically Enriched Categories

from Part 3 - Enrichment Of Diagrams And Mackey Functors In Closed Multicategories

Published online by Cambridge University Press:  16 January 2025

Niles Johnson
Affiliation:
Ohio State University
Donald Yau
Affiliation:
Ohio State University
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Summary

This chapter gives the basic definitions and results for enrichment in a nonsymmetric multicategory M. Proposition 6.2.1 shows that this material agrees, in the case that M is the endomorphism multicategory of a monoidal category, with classical enriched category theory over V. The main application takes M to be the multicategory of permutative categories and strictly unital symmetric monoidal functors, which is not an endomorphism multicategory. Sections 6.3 through 6.5 treat this case in detail.

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Chapter
Information
Homotopy Theory of Enriched Mackey Functors
Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors
, pp. 167 - 209
Publisher: Cambridge University Press
Print publication year: 2025

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