Actors in categories of interest

Casas, J. M.; Datuashvili, T.; Ladra, M.

Actors in categories of interest

Authors

Casas, J. M.

Datuashvili, T.

Ladra, M.

Description

For an object $A$ of a category of interest $\mathbb{C}$ we construct the group with operations ${\mathfrak{B}}(A)$ and the semidirect product ${\mathfrak{B}}(A)\ltimes A$ and prove that there exists an actor of $A$ in $\mathbb{C}$ if and only if ${\mathfrak{B}}(A)\ltimes A \in \mathbb{C}$. The cases of groups, Lie, Leibniz, associative, commutative associative, alternative algebras, crossed and precrossed modules are considered. The paper contains some results for the case $Ω_2 = \{+,*,*^{\circ}\}$.
31 pages