Crossed Modules of Monoids II: Relative Crossed Modules

Research output: Contribution to journalArticle


This is the second part of a series of three strongly related papers in which three equivalent structures are studied:Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans.Crossed modules of monoids relative to this class of spans.Simplicial monoids of so-called Moore length 1 relative to this class of spans. The most important examples of monoids that are covered are small categories (treated as monoids in categories of spans) and bimonoids in symmetric monoidal categories (regarded as monoids in categories of comonoids). In this second part we define relative crossed modules of monoids and prove their equivalence with the relative categories of Part I.

Original languageEnglish
JournalApplied Categorical Structures
Publication statusAccepted/In press - Jan 1 2020



  • Bimonoid
  • Crossed module
  • Internal category

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this