Segal conditions for generalized operads
arXiv:2208.13852 · doi:10.1090/conm/802/16077
Abstract
This note is an introduction to several generalizations of the dendroidal sets of Moerdijk--Weiss. Dendroidal sets are presheaves on a category of rooted trees, and here we consider indexing categories whose objects are other kinds of graphs with loose ends. We examine the Segal condition for presheaves on these graph categories, which is one way to identify those presheaves that are a certain kind of generalized operad (for instance wheeled properad or modular operad). Several free / forgetful adjunctions between different kinds of generalized operads can be realized at the presheaf level using only the left Kan extension / restriction adjunction along a functor of graph categories. These considerations also have bearing on homotopy-coherent versions of generalized operads, and we include some questions along these lines.
arXiv comment33 pages, 11 figures, comments and suggestions welcome. A companion to arXiv:2109.06231, intended for submission to a conference proceedings
References in corpus (28)
- Gromov-Witten classes, quantum cohomology, and enumerative geometry
- A Koszul duality for props
- Dendroidal Sets
- Dendroidal sets and simplicial operads
- Dendroidal sets as models for homotopy operads
- Monads with arities and their associated theories
- Homotopy theory for algebras over polynomial monads
- On an extension of the notion of Reedy category
- Wheeled PROPs, graph complexes and the master equation
- Infinity Properads and Infinity Wheeled Properads
- Operads revisited
- Monads and theories
- Operads for complex system design specification, analysis and synthesis
- Polycategories via pseudo-distributive laws
- A graphical category for higher modular operads
- On the category of props
- Dwyer--Kan homotopy theory for cyclic operads
- Modular operads and the nerve theorem
- A criterion for existence of right-induced model structures
- Higher cyclic operads
- 2-Segal spaces as invertible infinity-operads
- The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions
- Whole-grain Petri nets and processes
- On factorizations of graphical maps
- Graphical combinatorics and a distributive law for modular operads
- On rectification and enrichment of infinity properads
- Categories of graphs for operadic structures
- Lecture notes on infinity-properads