Authors: Čukić, Sonja Lj.
Petrić, Zoran 
Title: The n-fold reduced bar construction
Journal: Journal of Homotopy and Related Structures
Volume: 13
Issue: 3
First page: 503
Last page: 543
Issue Date: 1-Sep-2018
ISSN: 1512-2891
DOI: 10.1007/s40062-017-0191-1
This paper is about a correspondence between monoidal structures in categories and n-fold loop spaces. We developed a new syntactical technique whose role is to substitute the coherence results, which were the main ingredients in the proof that the Segal–Thomason bar construction provides an appropriate simplicial space. The results we present here enable more common categories to enter this delooping machine. For example, such as the category of finite sets with two monoidal structures brought by the disjoint union and Cartesian product.
Keywords: Bar construction | Infinite loop spaces | Monoidal categories
Publisher: Springer Link
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Representations of logical structures and formal languages and their application in computing 

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