Graphical calculus of Hopf crossed modules

Emir K.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.2, pp.695-707, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.467966
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.695-707
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

We give the graphical notion of crossed modules of Hopf algebras-will be called Hopf crossed modules for short- in a symmetric monoidal category. We use the web proof assistant Globular to visualize our (colored) string diagrams. As an application, we introduce the homotopy of Hopf crossed module maps via Globular, and give some of its functorial relations.