Actors in categories of interest

Details Actors in categories of interest Actors in categories of interest

2007-02-20

arxiv.org/abs/math/0702574v2

Mathematics

Category Theory

31 pages

Scientific paper

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 $\Omega_2 = \{+,*,*^{\circ}\}$.

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