Mathematical analysis reveals categorical equivalences across Lie algebraic homotopy 3-types, highlighting deep structural links among higher-dimensional crossed and simplicial modules.
In this work, we study the relationship among Lie algebraic homotopy 3-types. We investigate the categorical connection between crossed squares, internal crossed modules, 2-crossed modules, quadratic modules of Lie algebras, and simplicial and bisimplicial Lie algebras.
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YILMAZ et al. (2026) studied this question.
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