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Category of soft Lie algebra. (English) Zbl 1436.17042

Summary: 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 \({\mathbb{F}} \).

MSC:

17B99 Lie algebras and Lie superalgebras
18B99 Special categories
18G05 Projectives and injectives (category-theoretic aspects)
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