On the category of weak Cayley table morphisms between groups

• Autores: K.W. Johnson, Jonathan D. H. Smith
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 1, 2007, págs. 57-67
• Idioma: inglés
• DOI: 10.1007/s00029-007-0032-x
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• Resumen

  • Weak Cayley table functions between groups are generalized conjugacy-preserving homomorphisms, under which products of images are conjugate to images of products. There is a weak Cayley table bijection between two groups iff they have the same 2-characters. In this paper, weak Cayley table functions are augmented to include the specific conjugating elements, leading to the concept of a weak (Cayley table) morphism. If the conjugating elements are chosen subject to a crossed-product condition, then the weak morphisms between groups form a category. The forgetful functor to this category from the category of group homomorphisms is shown to possess a left adjoint. Two weak morphisms are said to be homotopic if they project to the same weak Cayley table function. As a first step in the analysis of the category of weak morphisms, the group of units of the monoid of weak morphisms homotopic to the identity automorphism of a group is described.