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--- Research
--- Preprints and articles in press
N. Bortolussi and M. Mombelli, The adjoint algebra for 2-categories.  Preprint arXiv:2005.05271
--- Publications
-  N. Bortolussi and M. Mombelli, The character algebra for module categories over Hopf algebras. Colloquium Mathematicum to appear. Preprint arxiv:1808.04810    pdf
- A. Mejía Castaño and M. Mombelli, Equivalence classes of exact module categories over graded tensor categories. Communications in Algebra 48 (2020) 4102-4131.    pdf
E. Bernaschini, C. Galindo and M. Mombelli, Group actions on 2-categories,  Manuscripta Math. 159, No. 1-2, 81–115 (2019).      pdf
M. Mombelli and S. Natale, Module categories over equivariantized tensor categories. Mosc. Math. J. 17 (1), 97-128 (2017)       pdf
  A. Mejía Castaño and M. Mombelli. Crossed extensions over the  corepresentation category of finite supergroup algebras. Int. J. Math. DOI :  10.1142/S0129167X15500676   pdf
M. Mombelli. The Brauer-Picard group of the representation category of finite supergroup algebras. Rev. Unión Mat. Argent. vol. 55 No. 1 (2014) 83-117.
-   B. Femic, A. Mejía Castaño y M. Mombelli. Invertible bimodule categories over the representation category of a Hopf  algebra.   J. Pure Appl. Algebra  218 (2014) 2096–2118.        pdf
M. Mombelli. Families of finite-dimensional Hopf algebras with the Chevalley property.  Algebr. Represent. Theory 16 (2013) 421-435. pdf
M. Mombelli. On the tensor product of bimodule categories over Hopf algebras.  Abhandlungen aus dem Math. Sem. der Universitat Hamburg  (82) 2012  173-192. pdf
O. Buerschaper, M. Christandl, M. Aguado and M. Mombelli. A hierarchy of topological tensor network states,  J. Math. Phys. 54, 012201 (2013); doi: 10.1063/1.4773316. pdf
C. Galindo and M. Mombelli. Module categories over finite pointed tensor categories  Selecta Mathematica NS. volume 18, issue 2 (2012) 357-389. pdf
A. García Iglesias and M Mombelli. Representations of the category of modules over pointed Hopf algebras over S_3 and S_4.  Pacific J. Math. vol 252 nº 2 (2011) 343-378.
M. Mombelli. Representations of tensor categories coming from quantum linear spaces. J. London Math. Soc. (2) 83 (2011) 19--35.
M. Mombelli. Module categories over pointed Hopf algebras. Mathematische Zeitschrift 266 nº2 (2010) 319-344.
M. Mombelli. Constructing dynamical twists over a non-abelian base. Applied Categorical Structures Volume 18 nº 4 (2010) 407-429.
M. Mombelli. Dynamical twists in Hopf algebras. Int. Math. Res. Not. (2007) vol. 2007.
N. Andruskiewitsch and M. Mombelli. On module categories over finite-dimensional Hopf algebras. J. Algebra 314 (2007) 383-418.
M. Mombelli and S. Natale. Tensor categories and vacant double groupoids. Math. Res. Lett. 14 (2007) 1-18.
C. Maldonado and M. Mombelli. On braided groupoids. J. Algebra 307 (2007) n° 2 677-694.
N. Andruskiewitsch and M. Mombelli. Examples of weak Hopf algebras arising from vacant double groupoids. Nagoya Math. J. 181 (2006) 1-27.
--- Other works
  M. Mombelli, Introducción a las categorías tensoriales y sus representaciones, notes in spanish (still in progress, possibly with errors)
  M. Mombelli and S. Simondi. Introduction to Galois theory. (In spanish) Trabajos de Matemática serie B 2011/58, FAMAF.
  M. Mombelli. Last Fermat theorem, Revista de Educación Matematica 22 (2007) No 1 (An  historical review).
M. Mombelli. Finite groups and their representations, Notes (in spanish) of a small course given at Universidad Sergio Arboleda, Bogotá, Colombia, january 2007.
--- Unpublished monographs
Categorías de fusión y grupoides cuanticos, Ph.D. thesis ( in spanish ) Fa.M.A.F. Universidad Nacional de Córdoba 2006.
Anillos simples y semisimples, first award in a monograph contest U.M.A. (2000).
--- Talks
Dynamical twists in finte-dimensional Hopf algebras, in the XVII Coloquio Latinoamericano de Algebra, Medellin, Colombia, july 2007.
Module categories over Hopf algebras and Yan-Zhu stabilizers, in New Techniques in Hopf algebras and graded ring theory, Brussels, Belgium, september 2006.
Talks given at Ludwig-Maximilians Universität, Munich.
Talk given at the Colloquium in Hopf algebras, quantum groups and tensor categories, La Falda, Córdoba, Argentina, September 2009.

Updated 09.08.2020