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2 results

  • CHARACTERIZING n-ISOCLINIC CLASSES OF CROSSED MODULES

  • Part of
  • HAJAR RAVANBOD, ALI REZA SALEMKAR, SAJEDEH TALEBTASH
  • Journal:
    Glasgow Mathematical Journal / Volume 61 / Issue 3 / September 2019
    Published online by Cambridge University Press:
    08 October 2018, pp. 637-656
    Print publication:
    September 2019
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  • In this paper, we introduce the notion of the equivalence relation, called n-isoclinism, between crossed modules of groups, and give some basic properties of this notion. In particular, we obtain some criteria under which crossed modules are n-isoclinic. Also, we present the notion of n-stem crossed module and, under some conditions, determine them within an n-isoclinism class.

  • Hopf Algebras of Combinatorial Structures

  • William R. Schmitt
  • Journal:
    Canadian Journal of Mathematics / Volume 45 / Issue 2 / 01 April 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 412-428
    Print publication:
    01 April 1993
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  • A generalization of the definition of combinatorial species is given by considering functors whose domains are categories of finite sets, with various classes of relations as moronisms. Two cases in particular correspond to species for which one has notions of restriction and quotient of structures. Coalgebras and/or Hopf algebras can be associated to such species, the duals of which provide an algebraic framework for studying invariants of structures.