Higher dimensional algebras via colored PROPs

2008/09/12 by Donald Yau, Yau, Donald
Mathematics · #18A05 #18D50 #55P99 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0809.2161

openalex publication_date 2008/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting from any unital colored PROP P, we define a category P(P) of shapes called P-propertopes. Presheaves on P(P) are called P-propertopic sets. For 0 ≤ n ≤ ∞ we define and study n-time categorified P-algebras as P-propertopic sets with some lifting properties. Taking appropriate PROPs P, we obtain higher categorical versions of polycategories, 2-fold monoidal categories, topological quantum field theories, and so on.

Citations

• A polarized view of string topology
• Notes on string topology

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