$1$-cohomology of simplicial amalgams of groups

TL;DR

This paper introduces a cohomological approach to classify simplicial amalgams of groups, extending the method to various categories and providing explicit computations for specific examples.

Contribution

It generalizes cohomological classification to simplicial amalgams in any concrete category, with explicit calculations for small simplices.

Findings

Developed a cohomological classification method for amalgams.

Generalized to simplicial amalgams in any concrete category.

Computed non-commutative 1-cohomology for specific examples.

Abstract

We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.