arXiv subjects

Simona Paoli

Publications and source records attributed to Simona Paoli.

21 records · Page 2Linked to original sources

arXiv2006

2-nerves for bicategories

We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. We define a 2-category NHom whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories, in such a way that the 2-nerve construction becomes a full embedding of NHom in the 2-category of simplicial objects in Cat. This embedding has a left biadjoint, and we characterize its image. The 2-nerve of a bicategory is always a weak 2-category in the sense of Tamsamani, and we show that NHom is biequivalent to a certain 2-category whose objects are Tamsamani weak 2-categories.

math.CT↗

arXiv2003

On the non-balanced property of the category of crossed modules in groups

An algebraic category $\mathcal{C}$ is called balanced if the cotriple cohomology of any object of $\mathcal{C}$ vanishes in positive dimensions on injective coefficient modules. Important examples of balanced and of non-balanced categories occur in the literature. In this paper we prove that the category of crossed modules in groups is non-balanced.

math.AT↗

arXiv2003

(Co)homology of crossed modules with coefficients in a $π_1$-module

We define a cotriple (co)homology of crossed modules with coefficients in a $π_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.

math.AT↗