## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 57-67 |

Number of pages | 11 |

Journal | Selecta Mathematica, New Series |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2007 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)