Generalized Enrichment for Categories and Multicategories

Abstract

In this paper we answer the question: `what kind of a structure can a general multicategory be enriched in?' The answer is, in a sense to be made precise, that a multicategory of one type can be enriched in a multicategory of the type one level up. In the case of ordinary categories this reduces to something surprising: a category may be enriched in an `fc-multicategory', a very general kind of 2-dimensional structure encompassing monoidal categories, plain multicategories, bicategories and double categories. (It turns out that fc-multicategories also provide a natural setting for the bimodules construction.) An extended application is given: the relaxed multicategories of Borcherds and Soibelman are explained in terms of enrichment.

79 pages

References in corpus (5)

• Quantum Cohomology of a Product
• General Operads and Multicategories
• Meromorphic tensor categories
• Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras
• On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani's weak n-categories

Cited by in corpus (8)

• Operads in Higher-Dimensional Category Theory
• Homotopy Algebras for Operads
• Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras
• The periodic table of $n$-categories for low dimensions II: degenerate tricategories
• Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets
• Weak n-categories: comparing opetopic foundations
• Relaxed multi category structure of a global category of rings and modules
• Generalized enrichment of categories