An infinity operad of normalized cacti

Luciana Basualdo Bonatto; Safia Chettih; Abigail Linton; Sophie Raynor; Marcy Robertson; Nathalie Wahl

doi:10.1016/j.topol.2022.108107

An infinity operad of normalized cacti

Luciana Basualdo Bonatto, Safia Chettih, Abigail Linton, Sophie Raynor, Marcy Robertson^*, Nathalie Wahl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We endow the normalized cacti with the structure of an ∞-operad by showing that its existing composition laws are associative up to all higher homotopies. The higher homotopies are encoded by a new topological operad of bracketed trees which we relate both to an enrichment of the dendroidal category Ω and to the Boardman-Vogt W-construction on the operad of operads.

Original language	English
Article number	108107
Pages (from-to)	1-54
Number of pages	54
Journal	Topology and its Applications
Volume	316
DOIs	https://doi.org/10.1016/j.topol.2022.108107
Publication status	Published - 1 Jul 2022

Keywords

Cactus operad
Infinity operads
Operads

Access to Document

10.1016/j.topol.2022.108107

Cite this

@article{750b4254a17f4b2794740ba0a9a132dc,

title = "An infinity operad of normalized cacti",

abstract = "We endow the normalized cacti with the structure of an ∞-operad by showing that its existing composition laws are associative up to all higher homotopies. The higher homotopies are encoded by a new topological operad of bracketed trees which we relate both to an enrichment of the dendroidal category Ω and to the Boardman-Vogt W-construction on the operad of operads.",

keywords = "Cactus operad, Infinity operads, Operads",

author = "\{Basualdo Bonatto\}, Luciana and Safia Chettih and Abigail Linton and Sophie Raynor and Marcy Robertson and Nathalie Wahl",

year = "2022",

month = jul,

day = "1",

doi = "10.1016/j.topol.2022.108107",

language = "English",

volume = "316",

pages = "1--54",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

}

TY - JOUR

T1 - An infinity operad of normalized cacti

AU - Basualdo Bonatto, Luciana

AU - Chettih, Safia

AU - Linton, Abigail

AU - Raynor, Sophie

AU - Robertson, Marcy

AU - Wahl, Nathalie

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We endow the normalized cacti with the structure of an ∞-operad by showing that its existing composition laws are associative up to all higher homotopies. The higher homotopies are encoded by a new topological operad of bracketed trees which we relate both to an enrichment of the dendroidal category Ω and to the Boardman-Vogt W-construction on the operad of operads.

AB - We endow the normalized cacti with the structure of an ∞-operad by showing that its existing composition laws are associative up to all higher homotopies. The higher homotopies are encoded by a new topological operad of bracketed trees which we relate both to an enrichment of the dendroidal category Ω and to the Boardman-Vogt W-construction on the operad of operads.

KW - Cactus operad

KW - Infinity operads

KW - Operads

UR - https://www.scopus.com/pages/publications/85130048258

UR - http://purl.org/au-research/grants/arc/DP160101519

UR - http://purl.org/au-research/grants/arc/FT160100393

U2 - 10.1016/j.topol.2022.108107

DO - 10.1016/j.topol.2022.108107

M3 - Article

AN - SCOPUS:85130048258

SN - 0166-8641

VL - 316

SP - 1

EP - 54

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 108107

ER -

An infinity operad of normalized cacti

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Enriched categories: Applications in geometry and logic

Monoidal categories and beyond: new contexts and new applications

Cite this

An infinity operad of normalized cacti

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Enriched categories: Applications in geometry and logic

Monoidal categories and beyond: new contexts and new applications

Cite this