Category of soft Lie algebra

Abstract

In this article, we consider category $${\mathbf {LA}}({\mathbb {F}})$$ of all Lie algebras over a field $${\mathbb {F}}$$ and Lie algebra homomorphisms and obtain some basic results of this category, such as the existence of product, equalizer, coequalizer, and pullback. Then, we introduce a subcategory of the category of soft sets, whose objects are soft Lie algebras and morphisms are soft Lie algebra homomorphisms and study some properties. In particular, we show that this category does not have a product. Also, we characterize injective objects in category soft set and category of soft Lie algebras over $${\mathbb {F}}$$.