Ideals and Congruences in L-algebras and Pre-L-algebras

2023/05/30 by Facchini, Alberto, Gran, Marino, Pompili, Mara
#Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2305.19042

Abstract

We link the recent theory of L-algebras to previous notions of Universal Algebra and Categorical Algebra concerning subtractive varieties, commutators, multiplicative lattices, and their spectra. We show that the category of L-algebras is subtractive and normal in the sense of Zurab Janelidze, but neither the category of L-algebras nor that of pre-L-algebras are Mal'tsev categories, hence in particular they are not semi-abelian. Therefore L-algebras are a rather peculiar example of an algebraic structure.

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