TY - JOUR

T1 - On the category of weak Cayley table morphisms between groups

AU - Johnson, K. W.

AU - Smith, J. D.H.

N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

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U2 - 10.1007/s00029-007-0032-x

DO - 10.1007/s00029-007-0032-x

M3 - Article

AN - SCOPUS:34249097748

SN - 1022-1824

VL - 13

SP - 57

EP - 67

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 1

ER -