Enrico Vitale - research
(All files are in pdf)
Degree Dissertation, Univ. di Milano 1989, Supervisor A. Carboni :
Equazionalità della logica via il calcolo delle relazioni.
Master Thesis, UCL 1992, Supervisor F. Borceux : Some remarks on Morita
theory.
Ph.D. Thesis, UCL 1994, Supervisor F.
Borceux : Left covering functors.
Books
1)
[with C. Centazzo] Sheaf theory, chapter VII in "Categorical
Foundations. Special Topics in Order, Topology, Algebra and Sheaf
Theory", M.C. Pedicchio and W. Tholen Editors, Encyclopedia of
Mathematics and its Applications 97, ISBN 0521834147, Cambridge
University Press (2003) 311-357.
2)
With J. Adamek and J. Rosicky: Algebraic Theories: A Categorical Introduction to General Algebra, with a Foreword by F.W. Lawvere, Cambridge Tracts in Mathematics 184, Cambridge University Press, 259 pages (2011).
(You can download here a preliminary
version, the final version is available via CUP.)
Publications
1)
[with F. Borceux] A Morita theorem in topology, Atti del V Convegno
Internazionale di Topologia in Italia (Lecce, 1990), Supplemento ai
Rendiconti del Circolo Matematico di Palermo II-29 (1992) pp.353-362.
2) Monoidal categories for
Morita theory, Cahiers de Topologie et
Géométrie Différentielle Catégoriques 33
(1992) 331-343.
3) [with F. Borceux] On the notion of
bimodel for functorial semantics,
Applied Categorical Structures 2 (1994) 283-295.
4)
On the characterization of monadic categories over Set, Cahiers de
Topologie et Géométrie Différentielle
Catégoriques 35 (1994) 351-358.
5)
[with F. Cagliari and S. Mantovani] Regularity of the category of
Kelley spaces, Applied Categorical Strctures 3 (1995) 357-361.
6)
Localizations of algebraic categories, Journal of Pure and Applied
Algebra 108 (1996) 315-320.
7)
The Brauer and Brauer-Taylor groups of a symmetric monoidal category,
Cahiers de Topologie et Géométrie Différentielle
Catégoriques 37 (1996) 91-122.
8)
[with A. Carboni] Regular and exact completions, Journal of Pure and
Applied Algebra 125 (1998) 79-116.
9)
[with F. Grandjean] Morita equivalence for regular algebras, Cahiers de
Topologie et Géométrie Différentielle
Catégoriques 39 (1998) 137-153.
10)
Localizations of algebraic categories II, Journal of Pure and Applied
Algebra 133 (1998) 317-326.
11)
[with M. Gran] On the exact completion of the homotopy category,
Cahiers de Topologie et Géométrie Différentielle
Catégoriques 39 (1998) 287-297.
12)
[with M. Gran] Localizations of Maltsev varieties, Theory and
Applications of Categories 5 (1999) 281-291.
13)
Multi-bimodels, Cahiers de Topologie et Géométrie
Différentielle Catégoriques 40 (1999) 284-296.
14)
[with S. Kasangian] Factorization systems for symmetric cat-groups,
Theory and Applications of Categories 7 (2000) 47-70.
15)
Quasi-varieties of presheaves, Theory and Applications of Categories 7
(2000) 236-238.
16)
[with M.C. Pedicchio] On the abstract characterization of
quasi-varieties, Algebra Universalis 43 (2000) 269-278.
17)
[with M.-A. Moens] Groupoids and the Brauer group, Cahiers de Topologie
et Géométrie Différentielle Catégoriques 41
(2000) 305-313.
18)
[with S. Lack] When do completion processes give rise to extensive
categories ? Journal of Pure and Applied Algebra 159 (2001) 203-230.
19)
Essential localizations and infinitary exact completion, Theory and
Applications of Categories 8 (2001) 465-480.
20)
[with J. Rosicky] Exact completion and representations in abelian
categories, Homology, Homotopy and Applications 3 (2001) 453-466.
21)
[with J. Adamek and J. Rosicky] On algebraically exact categories and
essential localizations of varieties, Journal of Algebra 244 (2001)
450-477.
22)
[with M. Grandis] A higher dimensional homotopy sequence, Homology,
Homotopy and Applications 4 (2002) 59-69.
23)
[with I. Le Creurer and F. Marmolejo] Beck's theorem for pseudo-monads,
Journal of Pure and Applied Algebra 173 (2002) 293-313.
24)
A Picard-Brauer exact sequence of categorical groups, Journal of Pure
and Applied Algebra 175 (2002) 383-408.
25) [with F. Borceux] Azumaya categories, Applied Categorical
Structures 10 (2002) 449-467.
26)
[with D. Bourn] Extensions of symmetric cat-groups, Homology, Homotopy
and Applications 4 (2002) 103-162.
27)
[with C. Centazzo] A duality relative to a limit doctrine, Theory and
Applications of Categories 10 (2002) 486-497.
28)
On the categorical structure of H^2, Journal of Pure and Applied
Algebra 177 (2003)
303-308.
29)
[with M. Dupont] Proper factorization systems in 2-categories, Journal
of Pure and Applied Algebra 179 (2003) 65-86.
30)
[with C. Centazzo and J. Rosicky] A characterization of locally
D-presentable categories, Cahiers de Topologie et
Géométrie Différentielle Catégoriques 45
(2004) 141-146.
31)
[with J. Duskin and R. Kieboom] Morphisms of 2-groupoids and
low-dimensional cohomology of crossed modules, Fields Institute
Communication Series 43 (2004) 227-241.
32)
[with S. Kasangian and S. Lack] Coalgebras, braidings, and distributive
laws,
Theory and Applications of Categories 13 (2004) 129-146.
33)
[with A. del Rio and J. Martinez Moreno] Chain complexes of symmetric
categorical groups, Journal of Pure and Applied Algebra 196 (2005)
279-312.
34)
[with S. Kasangian and G. Metere] Split extensions, semidirect product,
and holomorph of categorical groups, Homology, Homotopy
and Applications 8 (2006) 145-167.
35)
[with P. Carrasco and A.R. Garzon] Categorical crossed module, Theory
and Applications of Categories
16 (2006) 585-618.
36)
[with C. Centazzo] A classification of geometric morphisms and
localizations for presheaf categories and algebraic categories, Journal
of Algebra 303 (2006) 77-96.
37)
[with S. Kasangian, S. Mantovani and G. Metere] External derivations of
internal groupoids, Journal of Pure and Applied Algebra 212 (2008)
175-192.
38) [with J. Adamek and J. Rosicky] What are
sifted colimits? Theory
and Applications of Categories 23 (2010) 251-260.
39) Bipullbacks and calculus of fractions,
Cahiers de Topologie et
Géométrie Différentielle Catégoriques 51 (2010) 83-113.
40)
[with S. Kasangian and G. Metere]
The Ziqqurath of exact sequences of n-groupoids, Cahiers de Topologie et
Géométrie Différentielle Catégoriques 52 (2011) 2-44.
41) [with J. Adamek and J. Rosicky] Birkhoff 's variety theorem in many sorts, Algebra Universalis 68 (2012) 39-42.
42) [with O. Abbad, S. Mantovani and G. Metere] Butterflies in a semi-abelian context, Advances in Mathematics 238 (2013) 140-183.
43)
[with S. Mantovani and G. Metere] Profunctors in Maltcev categories and fractions of functors, Journal of Pure and Applied Algebra 217 (2013) 1173-1186.
44)
[with O. Abbad] Faithful calculus of fractions, Cahiers de Topologie et Géométrie Différentielle Catégoriques 54 (2013) 221-239.
Preprints
1]
[with A.R. Garzon] On the second cohomology categorical group and the Hochschild-Serre 2-exact sequence, (submitted).
2]
The snail lemma, (submitted).
3]
[with P.-A. Jacqmin] Bicategories of fractions for groupoids in monadic categories, (submitted).
4]
[with Z. Janelidze] Snail lemma in a pointed regular category,
(in preparation).
5]
[with S. Mantovani and G. Metere] The snail lemma for internal groupoids,
(in preparation).
[UCL]
[SC]
[MATH]
(c) 31 juillet 2014
