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Michel Hebert

Michel Hebert

  • Position: Professor Emeritus
  • Department: Department of Mathematics and Actuarial Science
  • Email: [email protected]
Brief Biography

Michel Hébert is professor emeritus in the mathematics and actuarial science department at The American University in Cairo. He has been with AUC since 1993, and has served as chair of the mathematics department for a total of seven years. Previously, Hébert was a faculty member at universities in Canada, Zambia and Gabon. He received his PhD from Laval University, in Quebec city, in 1984. Before this, Hébert studied at a navigation school, and traveled around the world as a seaman, and then as officer, in the Merchant Marine of various countries from 1970 to 1980.  

Research Interest

Category theory, mathematical logic, universal algebra. Particularly where any two of these three subjects intersect.

  • Hébert, M., "What is a finitely related object, categorically", Applied Categorical Structures, 21 (2013), 1-14. [Reviews: AMS: MR3010442 by S. Awodey; ZbIMath.: ZbI 1258.18001]
  • Hébert, M., "Weak reflections and weak factorization systems ", Applied Categorical Structures, 19 (2011), 9-38. [Reviews: AMS: MR2772600; ZblMath.: Zbl 1216.18001 by L.Scull ]
  • Hébert, M., "Finitely presentable morphisms in exact sequences", Theory and Applications of Categories 24 (2010), 209-220. [Reviews: AMS: MR2720183 by P. Gaucher; ZblMath.: Zbl 1231.18001 by W.Rump ]
  •  Adamek, J., Hébert, M., "On quasi-equations in locally presentable categories", Cahiers de Topologie et Géométrie Différentielle Catégoriques 50 (2009), 273-297. [Reviews: AMS: MR2589619 ; ZblMath.:Zbl 1188.18001 by M. Ojeda Aciego]
  •  Adamek , J., Hébert, M., Sousa, L., "The orthogonal subcategory problem and the small object argument", Applied Categorical Structures 17 (2009), 211-246. [Reviews:  AMS: MR2506255 by P. Gaucher; ZblMath.: Zbl 1194.18003 by J. Rosicky].
  •  Adamek, J., Hébert, M., Sousa, L., "A logic of injectivity " , Journal of Homotopy and Related Structures 2 (2007), special volume in honor of Saunders Mac Lane, 13-47. [Reviews: AMS: MR2369160, by H.Herrlich; ZblMath.: Zbl 1184.18002]
  • Villemaire, R., Hébert, M., " Theories of abelian groups and modules preserved under extensions ", in Löwe, Benedikt (ed.), Algebra, Logic, Set theory. Festschrift für Ulrich Felgner zum 65. Geburtstag. London: King's College Publications. Studies in Logic 4, 239-254, London 2007. [Reviews:  AMS: MR2412905 by Mike Prest; ZblMath.: Zbl 1147.03016, by P.C. Eklof]
  • Hébert, M., "\ lambda-presentable morphisms,  injectivity and weak factorization systems " ,  Applied Categorical Structures 14 (2006), 273-289. 371. [Reviews: AMS: MR2279587, by V. M. Gontineac ; ZblMath.: 1111.18002]
  • Adamek , J., Hébert, M., Sousa, L. , " A logic of orthogonality " , Archivum Mathematicum 42 (2006), no 4, 309-334. [Reviews: AMS: MR2283016 by S. Awodey; ZblMath.: Zbl 1156.18301]
  • Hébert, M., " K-purity and orthogonality " , Theory and Applications of Categories 12 (2004 ) , 355-371. [Reviews: AMS: MR2068519; ZblMath .: 1060.18001, by Y. Diers]
  • Hébert, M., "Algebraically closed and existentially closed substructures in categorical context" , Theory and Applications of Categories 12 (2004 ) , 270-298. [Reviews: AMS :MR2056100 (2005c:18005), by J. Rosicky ; ZblMath .: 1087.18001, by M. Eytan ]
  • Adamek , J., Hébert, M., Rosicky , J. "On abstract data-types presented by multiequations ", Theoretical Computer Science  275 (2002),  427-462. [Reviews: AMS :MR:2003g:68087 , by F. Gadducci ; ZblMath .: 1026.68031 (autorreferrat)]
  • Hébert, M., Rosicky , J. "Uncountable orthogonality is a closure property", Bulletin of the London Mathematical Society,  33 (2001), no.6,  685-688. [Reviews: AMS: MR:2002g:18007 , by C. Butz ; ZblMath .: 1031.18004, by Y. Diers ]
  • Hébert, M., Adamek, J., Rosicky, J. "More on orthogonality in locally presentable categories" , Cahiers de Topologie et Géometrie Différentielle Catégoriques 42 (2001), 51-80. [Reviews: AMS: MR :2001j:18013 ( autorreferrat ) ; ZblMath .: 0981.18007, by Horst Herrlich]
  • Hébert, M. "Concretely locally presentable and locally generated categories", Applied Categorical Structures 9 (2001), no.6, 595-623. [Reviews: AMS: MR :2002m:18005 , by F. Gadducci ; ZblMath .: 0998.18001, by J. Rosicky]
  • Adámek, J., Hébert, M., Rosicky , J. "On essentially algebraic theories and their generalisations ", Algebra Universalis 41 (1999), 213-227. [Reviews: AMS: MR :2000f:18005 , by R. Street; ZblMath.: 0970.18006, by J. Rachunek]
  •  Hébert, M. "On generation and implicit partial operations in locally presentable categories", Applied Categorical Sructures 6 (1998), 473-488. [Reviews: AMS: MR:99i:18002, by J. Isbell; ZblMath.:Zbl:913:18001, by J. Isbell]
  •  Hébert, M. "Purity and injectivity in accessible categories", Journal of Pure and Applied Algebra  129 (1998),143-147. [Reviews: AMS: MR:99c:18004, by T.H.Fay ;  ZblMath .: Zbl:934.18006, by J. Rosicky ]
  •  Hébert, M. "Syntactic characterization of closure under pullbacks and of locally polypresentable categories",  Annals of Pure and Applied Logic 84, No. 1 (1997), 73-95.   [Reviews: AMS.: MR:97j:03003 ( autorreferat );  ZblMath .: Zbl:870.18002, by H.-J.Vogel ]
  • Hébert, M. " Injectivity classes in abelian groups", Journal of the Egyptian Mathematical Society 5,  No. 1 (1997),  9-15. [Reviews: AMS: MR:99b:20089, by R. Gobel ; ZblMath .: Zbl:884.20033, by L.Bican ]
  • Hébert, M. "Sur les opérations partielles implicites et leur relation avec la surjectivité des épimorphismes",  Canadian Journal of Mathematics 45, No.3 (1993), 554-575. [Reviews: AMS: MR:94f:08007, by S. Comer;  ZblMath .: Zbl:798.08003 ( autorreferat )]
  • Hébert, M. "Representation and preservation of metamathematical quotients of A. Robinson", Algebra Universalis 30, No. 2 (1993),  294-296. [Reviews: AMS: MR:94g:03069, by G.Cherlin ; ZblMath .: Zbl:782.03015 ( autorreferat )]
  • Hébert, M. "Syntactic characterization of closure under connected limits", Archive for Mathematical Logic Vol. 31, No.2 (1991),  133-143. [Reviews: AMS.: MR:93e:03050 ( autorreferat ); ZblMath .: Zbl:781.03027 ( autorreferat )]
  • Hébert, M. "On the commutativity of ultraproducts with direct products", Proceedings of the American Mathematical Society, Vol. 113, No. 1 (1991), 213-216. [Reviews: AMS: MR:91k:03080 by F. Shen ;  ZblMath .: Zbl:727.03022 ( autorreferat )]
  • Hébert, M. "Sur le rang et la définissabilité des opérations implicites dans les classes d'algèbres", Colloquium Mathematicum, Vol. 58, Fasc.2 (1990), 175-188. [Reviews: AMS.: MR:91i:03065 by A.Blass ; ZblMath .: Zbl:715.08001 by R. Franci ]
  • Hébert, M. "On the fullness of certain functors ", Journal of Pure and Applied Algebra 61 (1989), 181-188. [Reviews: AMS.: MR:90j.18001 by K.I. Rosenthal; ZblMath .: Zbl:693.18001 by E. Giuli ]
  • Hébert, M., McKenzie, R.N. and Weaver, G.E. "Two definability results in the equational context", Proceedings of the American Mathematical Society 107 (1989), 47-53. [Reviews: AMS: MR:90b.08007 by S. Comer; ZblMath .: Zbl:684.03011 ( autorreferat )]
  • Hébert, M. "Generators, indecomposables and free algebras", Algebra Universalis 26, No 2 (1989), 137-142. [Reviews: AMS: MR:90e.08009 by M. Albert;  ZblMath .: Zbl:671.08008 by M. Stefanescu ]
  • Hébert, M. "Sur les algèbres libres pour les classes axiomatiques", Annales des sciences mathématiques  du Québec 13, No 1 (1989), 39-47. [Reviews: AMS.: MR:90i.08010 by J. Rosicky ;  ZblMath .: Zbl:689.08005 by K.I. Rosenthal]
  • Hébert, M. "Preservation and interpolation through binary relations between theories", Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35, No 2 (1989), 169-182. Corrections: 36 (1990), 373. [Reviews: AMS: MR:90c.03025 and 92g:03048 by T. Miyama; ZblMath .: Zbl:652.03021 ( autorreferat ); Philosopher's Index: Vol 23, 4, p.130 ( autorreferat )]
  • Hébert, M. Characterizations of axiomatic categories of models canonically isomorphic to (quasi-)  varieties",  Canadian Mathematical Bulletin 31, No 3 (1988), 287-300. [Reviews: AMS.: MR:90d.03064 by A. Blass; ZblMath .: Zbl:563.03017 ( autorreferat )]
  • Hébert, M. "On the reflective hull problem", Commentationes Mathematicae Universitatis Carolinae 28,  No 4 (1987), 603-606. [Reviews: AMS: MR:89c.18002 by H. Herrlich ;  ZblMath .: Zbl:644.18002 by Y. Diers ]
  • Hébert, M. " Multireflections and multifactorization systems", Demonstratio Mathematica 20, No 3-4 (1987),  501-517. [Reviews: AMS: MR:89g.18002 by C. Némethi ;  ZblMath .: Zbl:693.18002 by D.H. Van Osdol ]
  •  Hébert, M. " Sur l'existence des algèbres libres pour les théories négatives ",  Review of Research Faculty of Science Mathematics Series (University of Novi Sad) 18, No 3 (1988), 1-23. [Reviews: AMS: MR:92a:03044 by S. Comer; ZblMath .: Zbl:712.08010 ( autorreferat )]
  • Hébert, M. "Combinaisons de théorèmes d'interpolation et de préservation", Annales des sciences mathématiques du Québec 9, No 2 (1985), 175-183. [Reviews: AMS MR:87j.03034 by B.F. Nebres ;  ZblMath .: Zbl:601.03012 ( autorreferat )]
  • Cassidy, C., Hébert, M. and Kelly, G.M. "Reflective subcategories, localizations and factorization systems",  Journal of the Australian Mathematical Society 38 (1985), 287-329. [Reviews: AMS: MR: 86j.18001 by J. Adámek; ZblMath.: 573.18002 by N. Popescu ]
  • Hébert, M. "Un théorème de préservation pour les factorisations ", Mathematical Reports of the Academy of Science of Canada 6 , No 2 (1984), 39-42. [Reviews: AMS: MR:85h.03031 by D. Lascar;  ZblMath .: Zbl:532.03011 ( autorreferat )] 

Others (non-refereed) 

  • Adamek, J., Hébert, M., Rosicky, J. "A syntactic characterization of locally generated and locally multi-generated categories", Seminarberichte Fernuniversitat Hagen, Special Volume dedicated to D. Pamplun, 1998.
  • Hatcher, W.S., Hébert, M.,  Preservation Theory. Québec, Prépublications de l'Université Laval, No.94-17,  1994.  (A 230 page monograph)

Non-mathematical work