Inverting operations in operads

Maria Basterra; Irina Bobkova; Kate Ponto; Ulrike Tillmann; Sarah Yeakel

doi:10.1016/j.topol.2017.12.011

Inverting operations in operads

Maria Basterra, Irina Bobkova, Kate Ponto, Ulrike Tillmann, Sarah Yeakel

Mathematics

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

3 Scopus citations

Abstract

We construct a localization for operads with respect to one-ary operations based on the Dwyer-Kan hammock localization [2]. For an operad O and a sub-monoid of one-ary operations W we associate an operad LO and a canonical map O→LO which takes elements in W to homotopy invertible operations. Furthermore, we give a functor from the category of O-algebras to the category of LO-algebras satisfying an appropriate universal property.

Original language	English
Pages (from-to)	130-145
Number of pages	16
Journal	Topology and its Applications
Volume	235
DOIs	https://doi.org/10.1016/j.topol.2017.12.011
State	Published - Feb 15 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Hammock localization
Operads
Simplicial localization
Symmetric monoidal categories
Trees

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2017.12.011

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AU - Basterra, Maria

AU - Bobkova, Irina

AU - Ponto, Kate

AU - Tillmann, Ulrike

AU - Yeakel, Sarah

PY - 2018/2/15

Y1 - 2018/2/15

N2 - We construct a localization for operads with respect to one-ary operations based on the Dwyer-Kan hammock localization [2]. For an operad O and a sub-monoid of one-ary operations W we associate an operad LO and a canonical map O→LO which takes elements in W to homotopy invertible operations. Furthermore, we give a functor from the category of O-algebras to the category of LO-algebras satisfying an appropriate universal property.

AB - We construct a localization for operads with respect to one-ary operations based on the Dwyer-Kan hammock localization [2]. For an operad O and a sub-monoid of one-ary operations W we associate an operad LO and a canonical map O→LO which takes elements in W to homotopy invertible operations. Furthermore, we give a functor from the category of O-algebras to the category of LO-algebras satisfying an appropriate universal property.

KW - Hammock localization

KW - Operads

KW - Simplicial localization

KW - Symmetric monoidal categories

KW - Trees

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VL - 235

SP - 130

EP - 145

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Inverting operations in operads

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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