nLab Marino Gran

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Selected writings

On the exact completion of the classical homotopy category $Ho(Top)$ being a pretopos:

• Marino Gran, Enrico Vitale, On the exact completion of the homotopy category, Cahiers de Topologie et Géométrie Différentielle Catégoriques 39 4 (1998) 287-297 [numdam:CTGDC_1998__39_4_287_0]

On the category of internal categories in a Malcev category:

• Marino Gran, Internal categories in Mal’cev categories, Journal of Pure and Applied Algebra 143 1-3 (1999) 221-229 [doi:10.1016/S0022-4049(98)00112-1]

For the characterisation of categories which are localizations? of Maltsev varieties:

• Marino Gran and Enrico Vitale, Localizations of Maltsev varieties, Theory and Applications of Categories 5 12 (1999) 281-291 [TAC]

On regular categories and semi-abelian categories:

• Dominique Bourn, Marino Gran, Regular, Protomodular, and Abelian Categories, Chapter IV, pp.165-211 in: Maria Pedicchio, Walter Tholen (eds.), Categorical Foundations, Cambridge University Press 2004 (doi:10.1017/CBO9781107340985.007)

• Marino Gran, An introduction to regular categories, in: New Perspectives in Algebra, Topology and Categories, Coimbra Mathematical Texts, Springer (2021) [arXiv:2004.08964, ISBN:978-3-030-84319-9]

• Marino Gran, Florence Sterck, Joost Vercruysse, A semi-abelian extension of a theorem by Takeuchi, J. Pure Appl. Alg. 223, 10 (2019) 4171-4190, doi

• Tomas Everaert, Marino Gran, Tim Van der Linden, Higher Hopf Formulae for Homology via Galois Theory, Adv. Math. 223, 10 (2008) 4171-4190, doi

On Goursat categories:

• Marino Gran, Diana Rodelo, A New Characterisation of Goursat Categories, Applied Categorical Structures 20 (2012) 229–238 [doi:10.1007/s10485-010-9236-x]

On the Beck-Chevalley condition in Goursat categories:

• Marino Gran, Diana Rodelo, Beck-Chevalley condition and Goursat categories, Journal of Pure and Applied Algebra 221 10 (2017) 2445-2457 [arXiv:1512.04066, doi:10.1016/j.jpaa.2016.12.031]

Presenting a pretorsion theory on Cat whose torsion(-free) objects are the groupoids (skeletal categories, respectively), hence whose “trivial objects” are the skeletal groupoids:

• Francis Borceux, Federico Campanini, Marino Gran, Walter Tholen, Groupoids and skeletal categories form a pretorsion theory in $Cat$ [arXiv:2207.08487]

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