Coextended weak entwining structures

Authors: JOSÉ NICANOR ALONSO ÁLVAREZ, JOSÉ MANUEL FERNANDEZ VILABOA, RAMÓN GONZÁLEZ RODRÍGUEZ

Abstract: In this paper, we formulate the definition of coextended weak entwining structure in a strict monoidal category with equalizers. For a coextended weak entwining structure (A,D,\psi,\alpha), we introduce the notions of weak (D,\alpha)-cleft extension and weak (D,\alpha)-Galois extension (with normal basis), proving that weak (D,\alpha)-Galois extensions with normal basis are equivalent to weak (D,\alpha)-cleft extensions.

Keywords: Monoidal category, coextended weak entwining structure, weak cleft extension, weak Galois extension, normal basis

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