TL;DR
This paper extends the theory of operads to higher dimensions, allowing for operations between operations that model complex algebraic structures on varieties of arbitrary dimensions.
Contribution
It introduces a higher-dimensional operad framework that generalizes classical operads to include operations between operations in higher-dimensional algebraic contexts.
Findings
Develops a new higher-dimensional operad theory
Models algebraic structures on varieties of arbitrary dimensions
Provides a foundation for future higher-dimensional algebraic studies
Abstract
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked subvarieties of arbitrary codimension.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models