Weak Crossed Biproducts and Weak Projections

2009/06/09 by J. M. Fernández Vilaboa, Vilaboa, J. M. Fernández, R. González Rodrı́guez +3 · 1 citation
Mathematics · #16W30 #18D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0906.1693

openalex publication_date 2009/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the universal theory of weak crossed biproducts, and we prove that every weak projection of weak bialgebras induces an example of this crossed structure. As an example, we give the construction of a weak projection of a weak bialgebra associated to a groupoid that admits an exact factorization.

Cited by

• Regular pairings of functors and weak (co)monads

Related

• Comparison of two notions of weak crossed product
• Weak Hopf algebras arising from weak matched pairs
• Cleft extensions of weak Hopf algebras
• Equivalent crossed products and cross product bialgebras
• Cross Product Bialgebras - Part I