Dominique Bourn
- Grade : Professeur émérite
- Equipe : Algèbre
- Adresse : LMPA
Centre Universitaire de la Mi-Voix
50 rue F. Buisson
CS80699
62228 Calais - Bureau : -
- Email : Dominique.Bourn@univ-littoral.fr
- Téléphone :
- Page personnelle : http://www-lmpa.univ-littoral.fr/~bourn
Publications
Livres
- From groups to categorial algebra ( ), Birkhäuser/Springer, Cham, 10-6, 2017.
- Schreier split epimorphisms in monoids and in semirings ( ), Universidade de Coimbra, Departamento de Matemática, Coimbra, 11-6, 2013.
- Mal'cev, protomodular, homological and semi-abelian categories ( ), Kluwer Academic Publishers, volume 566, 47-9, 2004.
Articles de revues
- A note on the categorical congruence distributivity ( ), In Theory Appl. Categ., volume 34, 16-438, 2019.
- The $3\times3$ lemma in the $\Sigma$-Mal'tsev and $\Sigma$-protomodular settings. Applications to monoids and quandles ( ), In Homology Homotopy Appl., volume 21, 305-332, 2019.
- Suprema of equivalence relations and non-regular Goursat categories ( ), In Cah. Topol. Géom. Différ. Catég., volume 59, 142-194, 2018.
- Central reflections and nilpotency in exact Mal'tsev categories ( ), In J. Homotopy Relat. Struct., volume 12, 765-835, 2017.
- On the classification property of the group $Aut\,K$ and its generalizations ( ), In Not. S. Afr. Math. Soc., volume 47, 8-23, 2016.
- Partial linearity and partial natural Mal'tsevness ( ), In Theory Appl. Categ., volume 31, 15-418, 2016.
- A note on the abelianization functor ( ), In Comm. Algebra, volume 44, 2009-2033, 2016.
- Monoids and pointed $S$-protomodular categories ( ), In Homology Homotopy Appl., volume 18, 151-172, 2016.
- Normalizers and Split Extensions ( ), In Appl. Categ. Structures, volume 23, 753-776, 2015.
- A structural aspect of the category of quandles ( ), In J. Knot Theory Ramifications, volume 24, 1550060-35, 2015.
- Two ways to centralizers of equivalence relations ( ), In Appl. Categ. Structures, volume 22, 833-856, 2014.
- Schreier split epimorphisms between monoids ( ), In Semigroup Forum, volume 88, 739-752, 2014.
- Normality, commutation and suprema in the regular Mal'tsev and protomodular settings ( ), In Cah. Topol. Géom. Différ. Catég., volume 54, 243-263, 2013.
- A characterisation of the "Smith is Huq" condition in the pointed Mal'tsev setting ( ), In Cah. Topol. Géom. Différ. Catég., volume 54, 163-183, 2013.
- On the monad of internal groupoids ( ), In Theory Appl. Categ., volume 28, 5-150, 2013.
- Aspects of algebraic exponentiation ( ), In Bull. Belg. Math. Soc. Simon Stevin, volume 19, 823-846, 2012.
- Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible categories ( ), In J. Pure Appl. Algebra, volume 216, 1757-1767, 2012.
- Comprehensive factorization and $I$-central extensions ( ), In J. Pure Appl. Algebra, volume 216, 598-617, 2012.
- Categorical (binary) difference terms and protomodularity ( ), In Algebra Universalis, volume 66, 277-316, 2011.
- Centralizer and faithful groupoid ( ), In J. Algebra, volume 328, 43-76, 2011.
- Internal profunctors and commutator theory; applications to extensions classification and categorical Galois theory ( ), In Theory Appl. Categ., volume 24, 17-451, 2010.
- 2-catégories réductibles ( ), In Repr. Theory Appl. Categ., 1-38, 2010.
- Centralizers in action accessible categories ( ), In Cah. Topol. Géom. Différ. Catég., volume 50, 211-232, 2009.
- Subtractive categories and extended subtractions ( ), In Appl. Categ. Structures, volume 17, 317-343, 2009.
- Pointed protomodularity via natural imaginary subtractions ( ), In J. Pure Appl. Algebra, volume 213, 1835-1851, 2009.
- Approximate Mal'tsev operations ( ), In Theory Appl. Categ., volume 21, 8-152, 2008.
- The Mal'tsev operation on extensions ( ), In Cah. Topol. Géom. Différ. Catég., volume 49, 176-195, 2008.
- Mal'cev conditions revisited ( ), In Appl. Categ. Structures, volume 16, 723-733, 2008.
- Commutator theory, action groupoids, and an intrinsic Schreier-Mac Lane extension theorem ( ), In Adv. Math., volume 217, 2700-2735, 2008.
- Abelian groupoids and non-pointed additive categories ( ), In Theory Appl. Categ., volume 20, 4-48, 2008.
- Distributive law, commutator theory and Yang-Baxter equation ( ), In JP J. Algebra Number Theory Appl., volume 8, 145-163, 2007.
- Cohomology without projectives ( ), In Cah. Topol. Géom. Différ. Catég., volume 48, 104-153, 2007.
- Baer sums in homological categories ( ), In J. Algebra, volume 308, 414-443, 2007.
- Initial normal covers in bi-Heyting toposes ( ), In Arch. Math. (Brno), volume 42, 335-356, 2006.
- Torsion theories in homological categories ( ), In J. Algebra, volume 305, 18-47, 2006.
- Action groupoid in protomodular categories ( ), In Theory Appl. Categ., volume 16, 2-46, 2006.
- Normal subobjects of topological groups and of topological semi-abelian algebras ( ), In Topology Appl., volume 153, 1341-1364, 2006.
- Congruence distributivity in Goursat and Mal'cev categories ( ), In Appl. Categ. Structures, volume 13, 101-111, 2005.
- Catégorification de structures définies par monade cartésienne ( ), In Cah. Topol. Géom. Différ. Catég., volume 46, 2-52, 2005.
- On the direct image of intersections in exact homological categories ( ), In J. Pure Appl. Algebra, volume 196, 39-52, 2005.
- Fibration of points and congruence modularity ( ), In Algebra Universalis, volume 52, 403-429, 2004.
- Commutator theory in strongly protomodular categories ( ), In Theory Appl. Categ., volume 13, 2-27, 2004.
- Extensions with abelian kernels in protomodular categories ( ), In Georgian Math. J., volume 11, 645-654, 2004.
- Normal sections and direct product decompositions ( ), In Comm. Algebra, volume 32, 3825-3842, 2004.
- Protomodular aspect of the dual of a topos ( ), In Adv. Math., volume 187, 240-255, 2004.
- Characterization of protomodular varieties of universal algebras ( ), In Theory Appl. Categ., volume 11, 6-143, 2003.
- The denormalized $3\times3$ lemma ( ), In J. Pure Appl. Algebra, volume 177, 113-129, 2003.
- Extensions of symmetric cat-groups ( ), In Homology Homotopy Appl., volume 4, 103-162, 2002.
- Centrality and connectors in Maltsev categories ( ), In Algebra Universalis, volume 48, 309-331, 2002.
- Intrinsic centrality and associated classifying properties ( ), In J. Algebra, volume 256, 126-145, 2002.
- Central extensions in semi-abelian categories ( ), In J. Pure Appl. Algebra, volume 175, 31-44, 2002.
- Aspherical abelian groupoids and their directions ( ), In J. Pure Appl. Algebra, volume 168, 133-146, 2002.
- Centrality and normality in protomodular categories ( ), In Theory Appl. Categ., volume 9, 151-165, 2001/02.
- A categorical genealogy for the congruence distributive property ( ), In Theory Appl. Categ., volume 8, 14-391, 2001.
- $3\times3$ lemma and protomodularity ( ), In J. Algebra, volume 236, 778-795, 2001.
- $n$-groupoids from $n$-truncated simplicial objects as a solution to a universal problem ( ), In J. Pure Appl. Algebra, volume 154, 71-102, 2000.
- The structural nature of the nerve functor for $n$-groupoids ( ), In Appl. Categ. Structures, volume 8, 81-113, 2000.
- Normal functors and strong protomodularity ( ), In Theory Appl. Categ., volume 7, 9-206, 2000.
- Normal subobjects and abelian objects in protomodular categories ( ), In J. Algebra, volume 228, 143-164, 2000.
- Baer sums and fibered aspects of Mal'cev operations ( ), In Cahiers Topologie Géom. Différentielle Catég., volume 40, 297-316, 1999.
- Protomodularity, descent, and semidirect products ( ), In Theory Appl. Categ., volume 4, 2-37, 1998.
- Mal'cev categories and fibration of pointed objects ( ), In Appl. Categ. Structures, volume 4, 307-327, 1996.
- Polyhedral monadicity of $n$-groupoids and standardized adjunction ( ), In J. Pure Appl. Algebra, volume 99, 135-181, 1995.
- Note on a submonadicity ( ), In Cahiers Topologie Géom. Différentielle Catég., volume 33, 199-206, 1992.
- Another denormalization theorem for abelian chain complexes ( ), In J. Pure Appl. Algebra, volume 66, 229-249, 1990.
- Produits tensoriels cohérents de complexes de chaî ne ( ), In Bull. Soc. Math. Belg. Sér. A, volume 41, 219-247, 1989.
- The tower of $n$-groupoids and the long cohomology sequence ( ), In J. Pure Appl. Algebra, volume 62, 137-183, 1989.
- A right exactness property for internal categories ( ), In Cahiers Topologie Géom. Différentielle Catég., volume 29, 109-155, 1988.
- The shift functor and the comprehensive factorization for internal groupoids ( ), In Cahiers Topologie Géom. Différentielle Catég., volume 28, 197-226, 1987.
- Une théorie de cohomologie pour les catégories exactes ( ), In C. R. Acad. Sci. Paris Sér. I Math., volume 303, 173-176, 1986.
- La tour de fibrations exactes des $n$-catégories ( ), In Cahiers Topologie Géom. Différentielle Catég., volume 25, 327-351, 1984.
- A general formulation of homotopy limits ( ), In J. Pure Appl. Algebra, volume 29, 129-141, 1983.
- Une autre propriété universelle pour le champ associé ( ), In Cahiers Topologie Géom. Différentielle, volume 21, 403-410, 1980.
- Distributeurs et théorie de la forme ( ), In Cahiers Topologie Géom. Différentielle, volume 21, 161-189, 1980.
- Sur les ditopos ( ), In C. R. Acad. Sci. Paris Sér. A, volume 279, 911-913, 1974.
- Ditopos ( ), In C. R. Acad. Sci. Paris Sér. A, volume 279, 731-732, 1974.
- Analgèbres et catalgèbres ( ), In C. R. Acad. Sci. Paris Sér. A, volume 278, 317-320, 1974.
- Anadèses et catadèses naturelles entre $3$-foncteurs ( ), In C. R. Acad. Sci. Paris Sér. A-B, volume 277, 1025-1028, 1973.
- Natural anadeses and catadeses ( ), In Cahiers Topologie Géom. Différentielle, volume 14, 371-415, 1973.
- Anadèses et catadèses naturelles ( ), In C. R. Acad. Sci. Paris Sér. A-B, volume 276, 1401-1404, 1973.
- Triples $p$-structurés ( ), In Cahiers Topologie Géom. Différentielle, volume 13, 327-356, 1972.
- Sur les objets de Kleisli et d'Eilenberg-Moore dans une $2$-catégorie ( ), In C. R. Acad. Sci. Paris Sér. A-B, volume 275, 1041-1044, 1972.
- Triples $p$-structurés ( ), In C. R. Acad. Sci. Paris Sér. A-B, volume 274, 703-705, 1972.
- Sur les triples structurés ( ), In C. R. Acad. Sci. Paris Sér. A-B, volume 275, 255-258, 1972.
Chapitres de livres
- A note on the notion of characteristic subobject in the Mal'tsev and protomodular settings ( ), Chapter in Categorical methods in algebra and topology, Univ. Coimbra, Coimbra, volume 46, 67-91, 2014.
- Moore normalization and Dold-Kan theorem for semi-abelian categories ( ), Chapter in Categories in algebra, geometry and mathematical physics, Amer. Math. Soc., volume 431, 105-124, 2007.
- Split extension classifier and centrality ( ), Chapter in Categories in algebra, geometry and mathematical physics, Amer. Math. Soc., volume 431, 85-104, 2007.
- Categorical aspects of modularity ( ), Chapter in Galois theory, Hopf algebras, and semiabelian categories, Amer. Math. Soc., volume 43, 77-100, 2004.
- Commutator theory in regular Mal'cev categories ( ), Chapter in Galois theory, Hopf algebras, and semiabelian categories, Amer. Math. Soc., volume 43, 61-75, 2004.
- Regular, protomodular, and abelian categories ( ), Chapter in Categorical foundations, Cambridge Univ. Press, volume 97, 165-211, 2004.
- Low-dimensional geometry of the notion of choice ( ), Chapter in Category theory 1991 (Montreal, PQ, 1991), Amer. Math. Soc., volume 13, 55-73, 1992.
- Normalization equivalence, kernel equivalence and affine categories ( ), Chapter in Category theory (Como, 1990), Springer, volume 1488, 43-62, 1991.
- Pseudofunctors and nonabelian weak equivalences ( ), Chapter in Categorical algebra and its applications (Louvain-La-Neuve, 1987), Springer, volume 1348, 55-71, 1988.
- A canonical action on indexed limits: an application to coherent homotopy ( ), Chapter in Category theory (Gummersbach, 1981), Springer, volume 962, 23-32, 1982.
- A propos des ditopos ( ), Chapter in Nordwestdeutsches Kategorienseminar (Tagung, Bremen, 1976), Univ. Bremen, 11-25, 1976.
- Objets de Kleisli et d'Eilenberg-Moore d'un triple dans une $2$-catégorie ( ), Chapter in Esquisses mathématiques, No. 19, Exp. No. 1, Fac. Sci. Univ. Paris VII, Paris, 6-3, 1973.
Rapports
- Normalizers in the non-pointed case ( ), Technical report 528, LMPA, 2017.
- Internal equivalence relations, modular formula and Goursat condition in non-regular context ( ), Technical report 526, LMPA, 2016.
- A structural aspect of the category of quandles ( ), Technical report 513, LMPA, 2014.
- Mal'tsev reflection, $S-$Mal'tsev and $S-$protomodular categories ( ), Technical report 497, LMPA, 2014.
- A note on the notion of characteristic subobject in the Mal'tsev and protomodular settings ( ), Technical report 496, LMPA, 2014.
- Centralizers in Action Accessible Categories ( ), Technical report 344, LMPA, 2007.
- Abelian groupoids and non pointed additive categories ( ), Technical report 332, LMPA, 2007.
- Split extension classifier and centrality ( ), Technical report 261, LMPA, 2005.
- Characterizing Mal'Cev Characterizations ( ), Technical report 260, LMPA, 2005.
- Moore normalization and Dold-Kan theorem for semi-abelian categories ( ), Technical report 259, LMPA, 2005.
- Closure Operators and Torsion Theories for Topological Algebras ( ), Technical report 213, LMPA, 2004.
- On the direct image of intersections in the exact homological categories ( ), Technical report 210, LMPA, 2004.
- A note on the normal subobjects in the topological groups and in the topological semi-abelian algebras ( ), Technical report 209, LMPA, 2004.
- Commutator theory in strongly protomodular categories ( ), Technical report 208, LMPA, 2004.
- Normal Section and Direct Decomposition ( ), Technical report 179, LMPA, 2003.
- Commutator Theory in Regular Mal'cev Categories ( ), Technical report 177, LMPA, 2002.
- Categorical Aspects of Modularity ( ), Technical report 176, LMPA, 2002.
- Intrinsic centrality and associated classifying properties ( ), Technical report 153, LMPA, 2001.
- A categorical genealogy for the congruence distributive property ( ), Technical report 147, LMPA, 2001.
- Protomodular aspects of the dual of a topos ( ), Technical report 146, LMPA, 2001.
- Central extensions in semi-abelian categories ( ), Technical report 137, LMPA, 2000.
- Centrality and normality in protomodular categories ( ), Technical report 136, LMPA, 2000.
- Denormalized 3x3 lemma and (-regular categories ( ), Technical report 133, LMPA, 2000.
- 3x3 lemma and protomodularity ( ), Technical report 120, LMPA, 2000.
- Normal functor and strong protomodularity ( ), Technical report 117, LMPA, 1999.
- Aspherical Mal'cev groupoids and their directions ( ), Technical report 110, LMPA, 1999.
- Normal subobjects and abelian objects in protomodular categories ( ), Technical report 087, LMPA, 1999.
- Baer sums and fibred aspects of Mal'cev operations ( ), Technical report 082, LMPA, 1999.