L.M.P.A
Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

## Dominique Bourn

• Grade : Professeur émérite
• Equipe : Algèbre
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

1. From groups to categorial algebra (), Birkhäuser/Springer, Cham, 10-6, . [pdf]
2. Schreier split epimorphisms in monoids and in semirings (, , and ), Universidade de Coimbra, Departamento de Matemática, Coimbra, 11-6, .
3. Mal'cev, protomodular, homological and semi-abelian categories ( and ), Kluwer Academic Publishers, volume 566, 47-9, .

### Articles de revues

1. A note on the categorical congruence distributivity (), In Theory Appl. Categ., volume 34, 16-438, .
2. The $3\times3$ lemma in the $\Sigma$-Mal'tsev and $\Sigma$-protomodular settings. Applications to monoids and quandles ( and ), In Homology Homotopy Appl., volume 21, 305-332, . [pdf]
3. Suprema of equivalence relations and non-regular Goursat categories (), In Cah. Topol. Géom. Différ. Catég., volume 59, 142-194, .
4. Central reflections and nilpotency in exact Mal'tsev categories ( and ), In J. Homotopy Relat. Struct., volume 12, 765-835, . [pdf]
5. On the classification property of the group $Aut\,K$ and its generalizations (), In Not. S. Afr. Math. Soc., volume 47, 8-23, .
6. Partial linearity and partial natural Mal'tsevness (), In Theory Appl. Categ., volume 31, 15-418, .
7. A note on the abelianization functor ( and ), In Comm. Algebra, volume 44, 2009-2033, . [pdf]
8. Monoids and pointed $S$-protomodular categories (, , and ), In Homology Homotopy Appl., volume 18, 151-172, . [pdf]
9. Normalizers and Split Extensions ( and ), In Appl. Categ. Structures, volume 23, 753-776, . [pdf]
10. A structural aspect of the category of quandles (), In J. Knot Theory Ramifications, volume 24, 1550060-35, . [pdf]
11. Two ways to centralizers of equivalence relations (), In Appl. Categ. Structures, volume 22, 833-856, . [pdf]
12. Schreier split epimorphisms between monoids (, , and ), In Semigroup Forum, volume 88, 739-752, . [pdf]
13. Normality, commutation and suprema in the regular Mal'tsev and protomodular settings (), In Cah. Topol. Géom. Différ. Catég., volume 54, 243-263, .
14. A characterisation of the "Smith is Huq" condition in the pointed Mal'tsev setting (, and ), In Cah. Topol. Géom. Différ. Catég., volume 54, 163-183, .
15. On the monad of internal groupoids (), In Theory Appl. Categ., volume 28, 5-150, .
16. Aspects of algebraic exponentiation ( and ), In Bull. Belg. Math. Soc. Simon Stevin, volume 19, 823-846, .
17. Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible categories ( and ), In J. Pure Appl. Algebra, volume 216, 1757-1767, . [pdf]
18. Comprehensive factorization and $I$-central extensions ( and ), In J. Pure Appl. Algebra, volume 216, 598-617, . [pdf]
19. Categorical (binary) difference terms and protomodularity ( and ), In Algebra Universalis, volume 66, 277-316, . [pdf]
20. Centralizer and faithful groupoid (), In J. Algebra, volume 328, 43-76, . [pdf]
21. Internal profunctors and commutator theory; applications to extensions classification and categorical Galois theory (), In Theory Appl. Categ., volume 24, 17-451, .
22. 2-catégories réductibles ( and ), In Repr. Theory Appl. Categ., 1-38, .
23. Centralizers in action accessible categories ( and ), In Cah. Topol. Géom. Différ. Catég., volume 50, 211-232, .
24. Subtractive categories and extended subtractions ( and ), In Appl. Categ. Structures, volume 17, 317-343, . [pdf]
25. Pointed protomodularity via natural imaginary subtractions ( and ), In J. Pure Appl. Algebra, volume 213, 1835-1851, . [pdf]
26. Approximate Mal'tsev operations ( and ), In Theory Appl. Categ., volume 21, 8-152, .
27. The Mal'tsev operation on extensions (), In Cah. Topol. Géom. Différ. Catég., volume 49, 176-195, .
28. Mal'cev conditions revisited ( and ), In Appl. Categ. Structures, volume 16, 723-733, . [pdf]
29. Commutator theory, action groupoids, and an intrinsic Schreier-Mac Lane extension theorem (), In Adv. Math., volume 217, 2700-2735, . [pdf]
30. Abelian groupoids and non-pointed additive categories (), In Theory Appl. Categ., volume 20, 4-48, .
31. Distributive law, commutator theory and Yang-Baxter equation (), In JP J. Algebra Number Theory Appl., volume 8, 145-163, .
32. Cohomology without projectives ( and ), In Cah. Topol. Géom. Différ. Catég., volume 48, 104-153, .
33. Baer sums in homological categories (), In J. Algebra, volume 308, 414-443, . [pdf]
34. Initial normal covers in bi-Heyting toposes (, and ), In Arch. Math. (Brno), volume 42, 335-356, .
35. Torsion theories in homological categories ( and ), In J. Algebra, volume 305, 18-47, . [pdf]
36. Action groupoid in protomodular categories (), In Theory Appl. Categ., volume 16, 2-46, .
37. Normal subobjects of topological groups and of topological semi-abelian algebras (), In Topology Appl., volume 153, 1341-1364, . [pdf]
38. Congruence distributivity in Goursat and Mal'cev categories (), In Appl. Categ. Structures, volume 13, 101-111, . [pdf]
39. Catégorification de structures définies par monade cartésienne ( and ), In Cah. Topol. Géom. Différ. Catég., volume 46, 2-52, .
40. On the direct image of intersections in exact homological categories (), In J. Pure Appl. Algebra, volume 196, 39-52, . [pdf]
41. Fibration of points and congruence modularity (), In Algebra Universalis, volume 52, 403-429, . [pdf]
42. Commutator theory in strongly protomodular categories (), In Theory Appl. Categ., volume 13, 2-27, .
43. Extensions with abelian kernels in protomodular categories ( and ), In Georgian Math. J., volume 11, 645-654, .
44. Normal sections and direct product decompositions ( and ), In Comm. Algebra, volume 32, 3825-3842, . [pdf]
45. Protomodular aspect of the dual of a topos (), In Adv. Math., volume 187, 240-255, . [pdf]
46. Characterization of protomodular varieties of universal algebras ( and ), In Theory Appl. Categ., volume 11, 6-143, .
47. The denormalized $3\times3$ lemma (), In J. Pure Appl. Algebra, volume 177, 113-129, . [pdf]
48. Extensions of symmetric cat-groups ( and ), In Homology Homotopy Appl., volume 4, 103-162, .
49. Centrality and connectors in Maltsev categories ( and ), In Algebra Universalis, volume 48, 309-331, . [pdf]
50. Intrinsic centrality and associated classifying properties (), In J. Algebra, volume 256, 126-145, . [pdf]
51. Central extensions in semi-abelian categories ( and ), In J. Pure Appl. Algebra, volume 175, 31-44, . [pdf]
52. Aspherical abelian groupoids and their directions (), In J. Pure Appl. Algebra, volume 168, 133-146, . [pdf]
53. Centrality and normality in protomodular categories ( and ), In Theory Appl. Categ., volume 9, 151-165, .
54. A categorical genealogy for the congruence distributive property (), In Theory Appl. Categ., volume 8, 14-391, .
55. $3\times3$ lemma and protomodularity (), In J. Algebra, volume 236, 778-795, . [pdf]
56. $n$-groupoids from $n$-truncated simplicial objects as a solution to a universal problem (), In J. Pure Appl. Algebra, volume 154, 71-102, . [pdf]
57. The structural nature of the nerve functor for $n$-groupoids (), In Appl. Categ. Structures, volume 8, 81-113, . [pdf]
58. Normal functors and strong protomodularity (), In Theory Appl. Categ., volume 7, 9-206, .
59. Normal subobjects and abelian objects in protomodular categories (), In J. Algebra, volume 228, 143-164, . [pdf]
60. Baer sums and fibered aspects of Mal'cev operations (), In Cahiers Topologie Géom. Différentielle Catég., volume 40, 297-316, .
61. Protomodularity, descent, and semidirect products ( and ), In Theory Appl. Categ., volume 4, 2-37, .
62. Mal'cev categories and fibration of pointed objects (), In Appl. Categ. Structures, volume 4, 307-327, . [pdf]
63. Polyhedral monadicity of $n$-groupoids and standardized adjunction (), In J. Pure Appl. Algebra, volume 99, 135-181, . [pdf]
64. Note on a submonadicity (), In Cahiers Topologie Géom. Différentielle Catég., volume 33, 199-206, .
65. Another denormalization theorem for abelian chain complexes (), In J. Pure Appl. Algebra, volume 66, 229-249, . [pdf]
66. Produits tensoriels cohérents de complexes de chaî ne (), In Bull. Soc. Math. Belg. Sér. A, volume 41, 219-247, .
67. The tower of $n$-groupoids and the long cohomology sequence (), In J. Pure Appl. Algebra, volume 62, 137-183, . [pdf]
68. A right exactness property for internal categories (), In Cahiers Topologie Géom. Différentielle Catég., volume 29, 109-155, .
69. The shift functor and the comprehensive factorization for internal groupoids (), In Cahiers Topologie Géom. Différentielle Catég., volume 28, 197-226, .
70. Une théorie de cohomologie pour les catégories exactes (), In C. R. Acad. Sci. Paris Sér. I Math., volume 303, 173-176, .
71. La tour de fibrations exactes des $n$-catégories (), In Cahiers Topologie Géom. Différentielle Catég., volume 25, 327-351, .
72. A general formulation of homotopy limits ( and ), In J. Pure Appl. Algebra, volume 29, 129-141, . [pdf]
73. Une autre propriété universelle pour le champ associé (), In Cahiers Topologie Géom. Différentielle, volume 21, 403-410, .
74. Distributeurs et théorie de la forme ( and ), In Cahiers Topologie Géom. Différentielle, volume 21, 161-189, .
75. Sur les ditopos (), In C. R. Acad. Sci. Paris Sér. A, volume 279, 911-913, .
76. Ditopos (), In C. R. Acad. Sci. Paris Sér. A, volume 279, 731-732, .
77. Analgèbres et catalgèbres (), In C. R. Acad. Sci. Paris Sér. A, volume 278, 317-320, .
78. Anadèses et catadèses naturelles entre $3$-foncteurs (), In C. R. Acad. Sci. Paris Sér. A-B, volume 277, 1025-1028, .
79. Natural anadeses and catadeses (), In Cahiers Topologie Géom. Différentielle, volume 14, 371-415, .
80. Anadèses et catadèses naturelles (), In C. R. Acad. Sci. Paris Sér. A-B, volume 276, 1401-1404, .
81. Triples $p$-structurés (), In Cahiers Topologie Géom. Différentielle, volume 13, 327-356, .
82. 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, .
83. Triples $p$-structurés (), In C. R. Acad. Sci. Paris Sér. A-B, volume 274, 703-705, .
84. Sur les triples structurés (), In C. R. Acad. Sci. Paris Sér. A-B, volume 275, 255-258, .

### Chapitres de livres

1. 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, .
2. 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, .
3. Split extension classifier and centrality ( and ), Chapter in Categories in algebra, geometry and mathematical physics, Amer. Math. Soc., volume 431, 85-104, .
4. Categorical aspects of modularity ( and ), Chapter in Galois theory, Hopf algebras, and semiabelian categories, Amer. Math. Soc., volume 43, 77-100, .
5. Commutator theory in regular Mal'cev categories (), Chapter in Galois theory, Hopf algebras, and semiabelian categories, Amer. Math. Soc., volume 43, 61-75, .
6. Regular, protomodular, and abelian categories ( and ), Chapter in Categorical foundations, Cambridge Univ. Press, volume 97, 165-211, .
7. Low-dimensional geometry of the notion of choice (), Chapter in Category theory 1991 (Montreal, PQ, 1991), Amer. Math. Soc., volume 13, 55-73, .
8. Normalization equivalence, kernel equivalence and affine categories (), Chapter in Category theory (Como, 1990), Springer, volume 1488, 43-62, . [pdf]
9. Pseudofunctors and nonabelian weak equivalences (), Chapter in Categorical algebra and its applications (Louvain-La-Neuve, 1987), Springer, volume 1348, 55-71, . [pdf]
10. A canonical action on indexed limits: an application to coherent homotopy (), Chapter in Category theory (Gummersbach, 1981), Springer, volume 962, 23-32, .
11. A propos des ditopos (), Chapter in Nordwestdeutsches Kategorienseminar (Tagung, Bremen, 1976), Univ. Bremen, 11-25, .
12. 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, .

### Rapports

1. Normalizers in the non-pointed case (), Technical report 528, LMPA, . [pdf]
2. Internal equivalence relations, modular formula and Goursat condition in non-regular context (), Technical report 526, LMPA, . [pdf]
3. A structural aspect of the category of quandles (), Technical report 513, LMPA, . [pdf]
4. Mal'tsev reflection, $S-$Mal'tsev and $S-$protomodular categories (), Technical report 497, LMPA, . [pdf]
5. A note on the notion of characteristic subobject in the Mal'tsev and protomodular settings (), Technical report 496, LMPA, . [pdf]
6. Centralizers in Action Accessible Categories ( and ), Technical report 344, LMPA, .
7. Abelian groupoids and non pointed additive categories (), Technical report 332, LMPA, . [pdf]
8. Split extension classifier and centrality ( and ), Technical report 261, LMPA, .
9. Characterizing Mal'Cev Characterizations ( and ), Technical report 260, LMPA, .
10. Moore normalization and Dold-Kan theorem for semi-abelian categories (), Technical report 259, LMPA, .
11. Closure Operators and Torsion Theories for Topological Algebras ( and ), Technical report 213, LMPA, .
12. On the direct image of intersections in the exact homological categories (), Technical report 210, LMPA, .
13. A note on the normal subobjects in the topological groups and in the topological semi-abelian algebras (), Technical report 209, LMPA, .
14. Commutator theory in strongly protomodular categories (), Technical report 208, LMPA, .
15. Normal Section and Direct Decomposition ( and ), Technical report 179, LMPA, .
16. Commutator Theory in Regular Mal'cev Categories (), Technical report 177, LMPA, .
17. Categorical Aspects of Modularity ( and ), Technical report 176, LMPA, .
18. Intrinsic centrality and associated classifying properties (), Technical report 153, LMPA, .
19. A categorical genealogy for the congruence distributive property (), Technical report 147, LMPA, .
20. Protomodular aspects of the dual of a topos (), Technical report 146, LMPA, .
21. Central extensions in semi-abelian categories ( and ), Technical report 137, LMPA, .
22. Centrality and normality in protomodular categories ( and ), Technical report 136, LMPA, .
23. Denormalized 3x3 lemma and (-regular categories (), Technical report 133, LMPA, .
24. 3x3 lemma and protomodularity (), Technical report 120, LMPA, .
25. Normal functor and strong protomodularity (), Technical report 117, LMPA, .
26. Aspherical Mal'cev groupoids and their directions (), Technical report 110, LMPA, .
27. Normal subobjects and abelian objects in protomodular categories (), Technical report 087, LMPA, .
28. Baer sums and fibred aspects of Mal'cev operations (), Technical report 082, LMPA, .

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