Partial and unified crossed products are weak crossed products
  In [J.M. Fern\'andez Vilaboa, R. Gonz\'alez Rodr\'iguez and A.B. Rodr\'iguez Raposo: Preunits and weak crossed products. J. of Pure Appl. Algebra 213, 2244-2261 (2009)] the notion of a weak crossed product of an algebra by an object, both living in a monoidal category was presented. Unified crossed products defined in [A. Agore, G. Militaru: Extending structures II: The quantum version. arXiv:1011.2174v3 (2011)] and partial crossed products defined in [M. Muniz S. Alves, E. Batista, M. Dokuchaev, A. Paques: Twisted partial actions of Hopf algebras. preprint (2011)] are crossed product structures defined for a Hopf algebra and another object. In this paper we prove that unified crossed products and partial crossed products are particular instances of weak crossed products. 
J. M. Fern\'andez Vilaboa, R. Gonz\'alez Rodr\'iguez and A. B.   Rodr\'iguez Raposo
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