[1]    D. Arias and M. Ladra, Central extensions of precrossed modules, Appl.  Categ.  Structures 12(4) (2004), 339–354.
 [2]    D. Arias and M. Ladra, Baer invariants and cohomology of precrossed modules, Appl. Categ.  Structures 22(1) (2014), 289–304.
 [3]    M. Barr, ``Exact Categories'', Lecture Notes in Math. 236, Springer, Berlin, 1971, 1-120.
 [4]    F. Borceux and D. Bourn, ``Mal'cev, Protomodular, Homological and Semi-Abelian Categories'', Mathematics and its Applications, Kluwer, 2004.
 [5]    F. Borceux and G. Janelidze, ``Galois Theories'', Cambridge Stud. Adv. Math. 72, Cambridge University Press, 2001.
 [6]    D. Bourn, Normalization equivalence, kernel equivalence and affine categories, Lecture Notes in   Math.  1488 (1991), 43-62.
 [7]    D. Bourn, Mal’cev categories and fibration of pointed objects, Appl. Categ. Structures 4 (1996), 307-327.
 [8]    D. Bourn, Commutator theory in regular Mal’tsev categories, Fields Inst. Commun.  43 (2004), 61-75.
 [9]    D. Bourn, Fibration of points and congruence modularity, Algebra Universalis 52(4) (2004), 403-429.
 [10]    D. Bourn, Internal profunctors and commutator theory; applications to extensions classification and categorical Galois theory, Theory  Appl. Categ. 24(17) (2010), 451–488.
 [11]    D. Bourn and M. Gran, Central extensions in semi-abelian categories, J.  Pure Appl. Algebra 175(1-3) (2002), 31-44.
 [12]    D. Bourn, D and M. Gran, Centrality and normality in protomodular categories, Theory Appl. Categ. 9(8) (2002), 151–165.
 [13]    D. Bourn and M. Gran, Centrality and connectors in Maltsev categories, Algebra Universalis 48(3) (2002), 309-331.
 [14]    D. Bourn and M. Gran, Categorical aspects of modularity, Fields Inst.  Commun. 43 (2004), 77-100.
 [15]    D. Bourn and A. Montoli, Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible categories, J.  Pure  Appl. Algebra 216(8-9) (2012), 1757–1767.
 [16]    D. Bourn and D. Rodelo, Comprehensive factorization and I-central extensions, J.  Pure Appl. Algebra 216(3) (2012), 598–617.
 [17]    R. Brown and G. Janelidze, Van Kampen theorems for categories of covering morphisms in lextensive categories, J.  Pure Appl.  Algebra 119(3) (1997), 255-263.
 [18]    R. Brown and G. Janelidze, Galois theory of second order covering maps of simplicial sets, J.  Pure Appl. Algebra 135(1) (1999), 23-31.
 [19]    R. Brown and G. Janelidze, Galois theory and a new homotopy double groupoid of a map of spaces, Appl. Categ.  Structures 12 (2004), 63-80.
 [20]    M. Bunge and S. Lack, Van Kampen theorems for toposes, Adv.  Math.  179(2) (2003), 291-317.
 [21]    A. Carboni, Categories of affine spaces, J.  Pure Appl. Algebra 61(3) (1989), 243-250.
 [22]    A. Carboni and G. Janelidze, Decidable (=separable) objects and morphisms in lextensive categories, J.  Pure Appl. Algebra 110(3) (1996), 219-240.
 [23]    A. Carboni and G. Janelidze, Boolean Galois theories, Georgian Math. J.  9(4) (2002), 645-658 (Also preprint  Dept. Math. Instituto Superior Téchnico, Lisbon 15, 2002).
 [24]    A. Carboni, G. Janelidze, G.M. Kelly, and R. Paré, On localization and stabilization of factorization systems, Appl. Categ.  Structures 5 (1997), 1-58.
 [25]    A. Carboni, G. Janelidze, and A.R. Magid, A note on Galois correspondence for commutative rings, J.  Algebra 183 (1996), 266-272.
 [26]    A. Carboni, G.M. Kelly, and M.C. Pedicchio, Some remarks on Maltsev and Goursat categories, Appl. Categ.  Structures 1(4) (1993), 385-421.
 [27]    A. Carboni, J. Lambek, and M.C. Pedicchio, Diagram chasing in Mal’cev categories, J.  Pure Appl. Algebra 69(3) (1990), 271-284.
 [28]    A. Carboni, M.C. Pedicchio, and N. Pirovano, Internal graphs and internal groupoids in Mal’cev categories, CT1991 Proceedings, Canadian Math. Soc. Conf. Proc. 13 (1992), 97-109.
 [29]    J.M. Casas, E. Khmaladze, M. Ladra, and T. Van der Linden, Homology and central extensions of Leibniz and Lie n-algebras, Homology Homotopy Appl.  13(1) (2011), 59–74.
 [30]    J.M. Casas and T. Van der Linden, Universal central extensions in semi-abelian categories, Appl. Categ.  Structures 22(1) (2014), 253–268.
 [31]    D. Chikhladze, Monotone-light factorization for Kan fibrations of simplicial sets with respect to groupoids, Homology Homotopy Appl. 6(1) (2004), 501–505.
 [32]    C. Cassidy, M. Hébert, and G.M. Kelly, Reflective subcategories, localizations, and factorization systems, J.  Aust. Math.  Soc. (Series A) 38 (1985), 287-329.
 [33]    D. Chikhladze, Separable morphisms of simplicial sets, J.  Homotopy Relat. Struct. 1(1)  (2006), 169–173.
 [34]    M.M. Clementino, A note on the categorical van Kampen theorem, Topology  Appl.  158(7) (2011), 926–929.
 [35]    M.M. Clementino and D. Hofmann, Descent morphisms and a Van Kampen in categories of lax algebras, Topology  Appl. 159(9) (2012), 2310–2319.
 [36]    M.M. Clementino, D. Hofmann, and A. Montoli, Covering morphisms in categories of relational algebras, Appl. Categ.  Structures 22(5-6) (2014), 767–788.
 [37]    M. Duckerts-Antoine, ``Fundamental groups in E-semi-abelian categories'', PhD Thesis, Université catholique de Louvain, Louvain-la-Neuve, 2013.
 [38]    M. Duckerts, T. Everaert, and M. Gran, A description of the fundamental group in terms of commutators and closure operators, J.  Pure Appl. Algebra 216(8-9) (2012), 1837–1851.
 [39]    M. Duckerts-Antoine, Fundamental group functors in descent-exact homological categories, to appear (and available electronically as http://www.mat.uc.pt/preprints/ps/p1538.pdf).
 [40]    S. Eilenberg and S. Mac Lane, Natural isomorphisms in group theory, Proc. Natl. Acad. Sci. 28(12) (1942), 537-543.
 [41]    S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans.  Amer.  Math. Soc. 58(2) (1945), 231-294.
 [42]    V. Even, A Galois-theoretic approach to the covering theory of quandles, Appl. Categ. Structures 22(5-6) (2014), 817–831.
 [43]    V. Even and M. Gran, On factorization systems for surjective quandle homomorphisms, J.  Knot Theory  Ramifications 23(11) (2014), 1450060 (15 pages).
 [44]    V. Even and M. Gran, Closure operators in the category of quandles, Topology  Appl.  200(1) (2016), 237-250.
 [45]    V. Even, M. Gran, and A. Montoli, A characterization of central extensions in the variety of quandles, to appear in Theory Appl. Categ. 31(8) (2016), 201-216.
 [46]    T. Everaert, ``An approach to non-abelian homology based on Categorical Galois Theory'', PhD Thesis, Free University of Brussels, Brussels, 2007.
 [47]    T. Everaert, Higher central extensions and Hopf formulae, J.  Algebra 324(8) (2010), 1771–1789.
 [48]    T. Everaert, Higher central extensions in Mal'tsev categories, Appl. Categ.  Structures 22(5-6) (2014), 961–979.
 [49]    T. Everaert, J. Goedecke, and T. Van der Linden, Resolutions, higher extensions and the relative Mal'tsev axiom, J.  Algebra 371 (2012), 132–155.
 [50]    T. Everaert, J. Goedecke, and T. Van der Linden, The fundamental group functor as a Kan extension, Cah.  Topol. Géom. Différ.  Catég. 54(3) (2013), 185–210.
 [51]    T. Everaert and M. Gran, Precrossed modules and Galois theory, J.  Algebra 297(1) (2006), 292–309.
 [52]    T. Everaert and M. Gran, On low-dimensional homology in categories, Homology Homotopy Appl.  9(1) (2007), 275–293.
 [53]    T. Everaert and M. Gran, Homology of n-fold groupoids, Theory  Appl. Categ.  23(2) (2010), 22–41.
 [54]    T. Everaert and M. Gran, Monotone-light factorisation systems and torsion theories, Bull.  Sci.  Math. 137(8) (2013), 996-1006.
 [55]    T. Everaert and M. Gran, Protoadditive functors, derived torsion theories and homology, J.  Pure Appl. Algebra 219(8) (2015), 3629–3676.
 [56]    T. Everaert, M. Gran, and T. Van der Linden, Higher Hopf formulae for homology via Galois theory, Adv. Math.  217 (2008), 2231-2267.
 [57]    T. Everaert and T. Van der Linden, Baer invariants in semi-abelian categories I: General theory, Theory Appl. Categ. 12(1) (2004), 1-33.
 [58] T. Everaert and T. Van der Linden, A note on double central extensions in exact Mal'tsev categories, Cah.  Topol.  G'{e}om. Diff'{e}r. Cat'{e}g. LI 2 (2010), 143–153.
 [59]    T. Everaert and T. Van der Linden, Galois theory and commutators, Algebra Universalis 65(2) (2011), 161–177.
 [60]    T. Everaert and T. Van der Linden, Relative commutator theory in semi-abelian categories, J.  Pure Appl.  Algebra 216(8-9) (2012), 1791–1806.
 [61]    T.H. Fay, On commuting congruences in regular categories, Math.  Colloq.,  University of Cape Town 11 (1977), 13-31.
 [62]    T.H. Fay, On categorical conditions for congruences to commute, Algebra Universalis 8 (1978), 173-179.
 [63]    R. Freese and R. McKenzie, Commutator theory for congruence modular varieties, London Math.  Soc.  Lecture Note Ser. 125, Cambridge University Press, 1987.
 [64]    A. Fr"{o}hlich, Baer-invariants of algebras, Trans. Amer.  Math.  Soc.  109 (1963), 221-244.
 [65]    J. Funk and B. Steinberg, The universal covering of an inverse semigroup, Appl. Categ.  Structures 18(2) (2010), 135–163.
 [66]    J. Furtado-Coelho, ``Varieties of $Gamma$-groups and associated functors'', PhD Thesis, University of London, 1972.
 [67]    J. Furtado-Coelho, Homology and generalized Baer invariants, J.  Algebra 40 (1976), 596-609.
 [68]    J. Goedecke and T. Van der Linden, On satellites in semi-abelian categories: Homology without projectives, Math.  Proc. Cambridge Philos. Soc. 147(3) (2009), 629-657.
 [69]    M. Gran, ``Central extensions of internal groupoids in Maltsev categories'', PhD Thesis, Université Catholique de Louvain, Louvain-la-Neuve, 1999.
 [70]    M. Gran, Central extensions and internal groupoids in Maltsev categories, J.  Pure Appl. Algebra 155(2-3) (2001), 139–166.
 [71]    M. Gran, Commutators and central extensions in universal algebra, J.  Pure Appl.  Algebra 174(3) (2002), 249–261.
 [72]    M. Gran, Applications of categorical Galois theory in universal algebra, Fields Inst.  Commun.  43 (2004), 243-280.
 [73]    M. Gran, ``Structures galoisiennes dans les catégories algébriques et homologiques'', Habilitation à Diriger des Recherches, Université du Littoral Côte d'Opale, 2007.
 [74]    M. Gran and G. Janelidze, Covering morphisms and normal extensions in Galois structures associated with torsion theories, Cah. Topol. Géom. Différ.  Catég. 50(3) (2009), 171-188.
 [75]    M. Gran and S. Lack, Semi-localizations of semi-abelian categories, J.  Algebra 454 (2016), 206-232.
 [76]    M. Gran and D. Rodelo, Some remarks on pullbacks in Gumm categories, Textos  Mat.  46 (2014), University of Coimbra, 125-136 (Also available as arXiv:1408.1342v1 [math.CT] 6 Aug 2014).
 [77]    M. Gran and V. Rossi, Galois theory and double central extensions, Homology Homotopy Appl.  6(1) (2004), 283–298.
 [78]    M. Gran and V. Rossi, Torsion theories and Galois coverings of topological groups, J.  Pure Appl. Algebra 208(1) (2007), 135-151.
 [79]    M. Gran and T. Van der Linden, On the second cohomology group in semi-abelian categories, J.  Pure Appl.  Algebra 212(3) (2008), 636-651.
 [80]    M. Grandis and G. Janelidze, Galois theory of simplicial complexes, Topology  Appl.  132(3) (2003), 281-289.
 [81]    J.R.A. Gray and T. Van der Linden, Tim Peri-abelian categories and the universal central extension condition, J. Pure Appl. Algebra 219(7) (2015), 2506–2520.
 [82]    A. Grothendieck, Revêtements étales et groupe fondamental, SGA 1, exposé V, Lecture Notes in Math.  224, Springer, 1971.
 [83]    H.P. Gumm, An easy way to the commutator in modular varieties, Arch.  Math.  34(3) (1980), 220-228.
 [84]    H.P. Gumm, ``Geometrical methods in congruence modular algebra'', Mem.  Amer.  Math.  Soc.   286, 1983, 79 pages.
 [85]    J. Hagemann and C. Hermann, A concrete ideal multiplication for algebraic systems and its relationship to congruence distributivity, Arch.  Math. 32 (1979), 234-245.
 [86]    T. Heindel and P. Sobociński, Being van Kampen is a universal property, Log. Methods Comput. Sci.  7(1) (2011),  22 pages.
 
 [87]    P.J.  Higgins, Groups with multiple operators, Proc. London Math.  Soc.  3(6) (1956), 366-416.
 [88]    G. Janelidze, Magid's theorem in categories, Bull. Georgian Acad.  Sci.  114(3) (1984), 497-500 (in Russian).
 [89]    G. Janelidze, Abelian extensions (of invertible rank, with normal basis) of commutative rings with an infinite number of idempotents, Proc. Math. Inst. Georgian Acad. Sci. LXXVII (1985), 36-49 (in Russian).
 [90]    G. Janelidze, The fundamental theorem of Galois theory, Math. USSR Sbornik 64(2) (1989), 359-384.
 [91]    G. Janelidze, Galois theory in categories: the new example of differential fields, Proceedings of the  Conference on  Categorical Topology,  Prague 1988, World Scientific 1989, 369-380.
 [92]    G. Janelidze, Pure Galois theory in categories, J.  Algebra 132 (1990), 270-286.
 [93]    G. Janelidze, Internal categories in Mal’tsev varieties, York University Preprint, Toronto, 1990.
 [94]    G. Janelidze, What is a double central extension? (the question was asked by Ronald Brown), Cah.  Topol.  Géom. Différ.  Catég. XXXII-3 (1991), 191-202.
 [95]    G. Janelidze, Precategories and Galois theory, Lecture Notes in Math. 1488 (1991), 157-173.
 [96]    G. Janelidze, A note on Barr-Diaconescu covering theory, Contemp.  Math.  131(3) (1992), 121-124.
 [97]    G. Janelidze, Internal crossed modules, Georgian Math. J.  10(1) (2003), 99-114.
 [98]    G. Janelidze, Categorical Galois theory: revision and some recent developments, Galois Connections and Applications, Kluwer Academic Publishers B.V., 2004, 139-171.
 [99]    G. Janelidze, Galois groups, abstract commutators, and Hopf formula, Appl. Categ.  Structures 16(6) (2008), 653-761.
 [100]    G. Janelidze, Light morphisms of generalized T0-reflections, Topology  Appl. 156(12) (2009), 2109-2115.
 [101]    G. Janelidze and G.M. Kelly, Galois theory and a general notion of a central extension, J. Pure Appl.  Algebra 97(2) (1994), 135-161.
 [102]    G. Janelidze and G.M. Kelly, The reflectiveness of covering morphisms in algebra and geometry, Theory Appl.  Categ.  3 (1997), 132-159.
 [103]    G. Janelidze and G.M. Kelly, Central extensions in universal algebra: a unification of three notions, Algebra Universalis 44 (2000), 123-128.
 [104]    G. Janelidze and G.M. Kelly, Central extensions in Mal’tsev varieties, Theory Appl. Categ.  7(10) (2000), 219-226.
 [105]    G. Janelidze, L. Márki, and W. Tholen, Locally semisimple coverings, J.  Pure  Appl. Algebra 128(3) (1998), 281-289.
 [106]    G. Janelidze, L. Márki, and W. Tholen, Semi-abelian categories, J.  Pure Appl.  Algebra 168(2-3) (2002), 367-386.
 [107]    G. Janelidze and M.C. Pedicchio, Internal categories and groupoids in congruence modular varieties, J.  Algebra 193 (1997), 552-570.
 [108]    G. Janelidze and M.C. Pedicchio, Pseudogroupoids and commutators, Theory Appl.  Categ.  8(15) (2001), 408-456.
 [109]    G. Janelidze, D. Schumacher, and R.H. Street, Galois theory in variable categories, Appl. Categ.  Structures
 1(1) (1993), 103-110.
 [110]    G. Janelidze and R.H. Street, Galois theory in symmetric monoidal categories, J. Algebra 220 (1999), 174-187.
 [111]    G. Janelidze and W. Tholen, Functorial factorization, well-pointedness and separability, J.  Pure Appl. Algebra 142(2) (1999), 99-130.
 [112]    G. Janelidze and W. Tholen, Extended Galois theory and dissonant morphisms, J.  Pure Appl.  Algebra 143(1-3) (1999), 231-253.
 [113]    [JT2010] G. Janelidze and W. Tholen, Strongly separable morphisms in general categories, Theory  Appl.  Categ.  23(5) (2010), 136-149.
 [114]    Z. Janelidze, Categorical terms for the shifting lemma, to appear.
 [115]    T. Janelidze-Gray, Composites of central extensions form a relative semi-abelian category, Appl. Categ.  Structures 22(5-6) (2014), 857-872.
 [116]    M. Jibladze and T. Pirashvili, Linear extensions and nilpotence of Maltsev theories, Beitr.  Algebra Geom. 46(1) (2005), 71–102.
 [117]    P.T. Johnstone, Affine categories and naturally Mal’tsev categories, J.  Pure Appl. Algebra 61(3) (1989), 251-256.
 [118]    E.W. Kiss, Three remarks on the modular commutator, Algebra Universalis 29(4) (1992), 455-476
 [119]    A. Kock, Generalized fibre bundles, Lecture Notes in Math. 1348 (1988),  Springer,  194-207.
 [120]    A. S.-T. Lue, Baer-invariants and extensions relative to a variety, Proc. Cambridge Philos. Soc. 63 (1967), 569-578.
 [121]    A. S.-T. Lue, Cohomology of groups relative to a variety, J.  Algebra 69 (1981), 155-174.
 [122]    S. Mac Lane, Groups, categories, and duality, Proc. Natl. Acad. Sci. U.S.A. 47 (1948), 263–267.
 [123]    S. Mac Lane, Duality for groups, Bull. Amer.  Math. Soc. 56 (1950), 485-516.
 [124]    S. Mac Lane, Categorical algebra, Bull.  Amer. Math. Soc. 71 (1965), 40-106.
 [125]    S. Mac Lane, ``Categories for the Working Mathematician'', Springer, 1971; 2nd Edition 1998.
 [126]    A.R. Magid, ``The separable Galois theory of commutative rings'', Marcel Dekker, 1974.
 [127]    A.R. Magid, The separable Galois theory of commutative rings, 2nd Edition, Pure Appl. Math. (Boca Raton), CRC Press, Boca Raton, FL, 2014.
 [128]    J. Meisen, ``Relations in categories'', PhD Thesis, McGill University, Montreal, 1972.
 [129]    J. Meisen, Relations in regular categories, Lecture Notes in Math.  418 (1974), Springer,  96-102.
 [130]    A. Montoli, D. Rodelo, and T. Van der Linden, A Galois theory for monoids, Theory Appl.  Categ.  29(7) (2014), 198–214.
 [131]    M.C. Pedicchio, Maltsev categories and Maltsev operations, J. Pure Appl. Algebra 98(1) (1995), 67-71.
 [132]    M.C. Pedicchio, A categorical approach to commutator theory, J.  Algebra 177 (1995), 647-657.
 [133]    M.C. Pedicchio, Arithmetical categories and commutator theory, Appl. Categ.  Structures 4(2-3) (1996), 297-305.
 [134]    M.C. Pedicchio, Some remarks on internal pregroupoids in varieties, Comm.  Algebra 26(6) (1998), 1737-1744.
 [135]    G. Peschke, Universal extensions, Comptes Rendus Math. Acad. Sci., Paris 349 (9-10) (2011), 501–504.
 [136]    D. Rodelo and T. Van der Linden, The third cohomology group classifies double central extensions, Theory Appl.  Categ. 23(8) (2010), 150–169.
 [137]    D. Rodelo and T. Van der Linden, Higher central extensions via commutators, Theory Appl.  Categ.  27 (2012), 189–209.
 [138]    D. Rodelo and T. Van der Linden, Higher central extensions and cohomology, Adv. Math. 287 (2016), 31–108.
 [139]    V. Rossi, Admissible Galois structures and coverings in regular Mal'{c}ev categories, Appl. Categ.  Structures 14(4) (2006), 291–311.
 [140]    V. Rossi, ``Galois structures and coverings in universal and topological algebra'', PhD Thesis, Udine, 2006.
 [141]    J.D.H. Smith, ``Mal’cev Varieties'', Lecture Notes in Math. 554, Springer, 1976.
 [142]    A. Szendrei, ``Commutators and compatible operations'', First Thomasina Coverly Memorial Workshop on Ordered Sets and Universal Algebra, Vanderbilt University, Nashville, TN, USA, May 24-27, 2000.
 [143]     J.J. Xarez, The monotone-light factorization for categories via preorders, Fields Inst. Commun. 43 (2004), 533-541.
 [144]     J.J. Xarez, Separable morphisms of categories via preordered sets, Fields Inst. Commun. 43 (2004), 543-549.
 [145]     J.J. Xarez, Internal monotone-light factorization for categories via preorders, Theory  Appl. Categ. 13(15) (2004), 235–251.
 [146]     J.J. Xarez, A Galois theory with stable units for simplicial sets,  Theory Appl.  Categ. 15(7) (2005/6), 178–193.
 [147]     J.J. Xarez, Well-behaved epireflections for Kan extensions, Appl. Categ.  Structures 18(2) (2010), 219–230.
 [148]     J.J. Xarez, Concordant and monotone morphisms, Appl. Categ. Structures 21(4) (2013), 393–415.
 [149]     I.A. Xarez and J.J. Xarez, Galois theories of commutative semigroups via semilattices, Theory Appl.  Categ.  28(33) (2013), 1153–1169.