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Nonabelian $H^2$ with coefficients in a group and with coefficients in a crossed module

Mikhail Borovoi

Abstract

In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.

Nonabelian $H^2$ with coefficients in a group and with coefficients in a crossed module

Abstract

In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian , using nonabelian with coefficients in crossed modules.

Paper Structure

This paper contains 8 sections, 5 theorems, 86 equations.

Table of Contents

  1. Second cohomology with coefficients in a crossed module
  2. Second cohomology with coefficients in a group
  3. Cohomology exact sequence
  4. A version of Theorem \ref{['t:DD']}.
  5. Example
  6. Checks in Construction \ref{['cons:action']}
  7. Checks in the proof of Theorem \ref{['t:Deb']}
  8. Proof of Theorem \ref{['t:DD']}

Key Result

Theorem 2.2

The canonical surjection e:lambda is a bijection.

Theorems & Definitions (15)

  • Definition 1.1
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Definition 2.1
  • Theorem 2.2: Debremaeker Debremaeker-thesis
  • proof : First proof
  • Theorem 3.1: Dedecker Dedecker69 and Debremaeker Debremaeker-thesis
  • proof
  • ...and 5 more