Segal Theta_2-monoids as monoidal (infty,1)-categories

In this thesis we establish a model structure for (infty, 2)-categories with a single object based on Theta_2-spaces with prescribed Segal and completeness conditions. Then we build a chain of Quillen equivalences between the previously mentioned model and a model for monoidal (infty, 1)-categories, where we use the category of complete Segal spaces. The comparison of models extends the categorical principle that monoids correspond to categories with one object, adapting it to the realm of higher categories.

Institutions

Publication Details

Journal
Libra
Published
2025-08-02
DOI
https://doi.org/10.18130/nwmc-xk89
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Segal Theta_2-monoids as monoidal (infty,1)-categories

Libra
Homotopy and Cohomology in Algebraic Topology
article

Segal Theta_2-monoids as monoidal (infty,1)-categories

article en

Abstract

In this thesis we establish a model structure for (infty, 2)-categories with a single object based on Theta_2-spaces with prescribed Segal and completeness conditions. Then we build a chain of Quillen equivalences between the previously mentioned model and a model for monoidal (infty, 1)-categories, where we use the category of complete Segal spaces. The comparison of models extends the categorical principle that monoids correspond to categories with one object, adapting it to the realm of higher categories.

Libra
University of Virginia (US)
Reduced inequalities
Openalex Percentile: Top 48%
Homotopy and Cohomology in Algebraic Topology
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Segal Theta_2-monoids as monoidal (infty,1)-categories · Libra (2025) | TGRS Research Map | TGRS