Marco Grandis, Università di Genova. Books, articles and preprints

I. Books

                                           

                                           

                                           

1. M. Grandis, Directed Algebraic Topology, Models of non-reversible worlds, Cambridge University Press, 2009. x + 434 pp.
Information at Cambridge U.P.:   hardback edition, e-book edition.
Free on line version, by agreement with Cambridge U.P. (since November 2011): Notice.

2. M. Grandis, Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups, World Scientific Publishing Co., 2012. xii + 369 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Preface and Contents.

3. M. Grandis, Homological Algebra in strongly non-abelian settings, World Scientific Publishing Co., 2013. xii + 343 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Preface and Contents.

4. M. Grandis, Category Theory and Applications: A textbook for beginners, World Scientific Publishing Co., 2018. x + 294 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

5. M. Grandis, Higher Dimensional Categories, From Double to Multiple Categories, World Scientific Publishing Co., 2020. xi + 522 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

6. M. Grandis, An Elementary Overview of Mathematical Structures. Algebra, Topology and Categories, World Scientific Publishing Co., 2021. x + 382 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

7. M. Grandis, Manifolds and Local Structures. A General Theory, World Scientific Publishing Co., 2021. xii + 362 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

8. M. Grandis, Category Theory and Applications: A textbook for beginners, Second Edition, World Scientific Publishing Co., 2021. xi + 377 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

9. M. Grandis, Algrebraic Topology: A structural introduction, World Scientific Publishing Co., 2022. x + 362 pp.
Information at World Scientific P.C.: hardback and e-book edition.
Introduction.

II. Editing
Guest Editor of two special issues:

1. Homotopy theory, Appl. Categ. Struct. 12 (2004), n.1.
Preface at: APCS. Also available here, in pdf.

2. Directed Algebraic Topology and Category Theory, Appl. Categ. Struct. 15 (2007), n. 4.
Preface at: APCS. Also available here, in pdf.

III. Articles and preprints, in reverse chronological order
All recent papers and some old ones can be downloaded.
The list includes some old preprints and articles, referred to in recent papers, which have been slightly revised, recently, and made available. For instance, [32a] is a revised version of [32].

[110] M. Grandis, The topology of critical processes, I (Processes and models) Cah. Topol. Géom. Diff. Catég. 65 (2024), 3--34.
Available at Cahiers (first article in this file).

[109] M. Grandis - G. Janelidze, From torsion theories to closure operators and factorization systems, Categ. Gen. Algebr. Struct. Appl. 12 (2020), 89--121.
Online publication (2019) at CGASA

[108] M. Grandis - R. Paré, Persistent double limits, Cah. Topol. Géom. Diff. Catég. 60 (2019), 255--297.
Available at Cahiers (in: Issue 3, second article).

[107] M. Grandis - G. Janelidze - L. Márki, Two- and one-dimensional combinatorial exactness structures in Kurosh-Amitsur radical theory, I, Cah. Topol. Géom. Différ. Catég. 58 (2017), 165--188.
Available at Cahiers (in: Issue 3-4, first article).

[106] M. Grandis - R. Paré, A multiple category of lax multiple categories, Cah. Topol. Géom. Diff. Catég. 58 (2017), 195--212.
Available at Cahiers (in: Issue 3-4, third article).
Based on a more extended preprint: 'Multiple categories of generalised quintets',
Pubbl. Mat. Univ. Genova, Preprint 607 (2017). Available in pdf.

[105] M. Grandis - R. Paré, Span and cospan representations of weak double categories, Categ. Gen. Algebr. Struct. Appl. 6 (2017), 85--105.
Online publication (18 Nov 2016) at CGASA.

[104] M. Grandis - R. Paré, Adjoints for multiple categories (On weak and lax multiple categories, III), Cah. Topol. Géom. Diff. Catég. 58 (2017), 3--48.
Available at Cahiers (in: Issue 1, first article).

[103] M. Grandis - R. Paré, Limits in multiple categories (On weak and lax multiple categories, II), Cah. Topol. Géom. Diff. Catég. 57 (2016), 163--202.
Available at Cahiers (in: Issue 3, first article).

[102] M. Grandis - R. Paré, An introduction to multiple categories (On weak and lax multiple categories, I), Cah. Topol. Géom. Diff. Catég. 57 (2016), 103--159.
Available at Cahiers (in: Issue 2, second article).

[101] M. Grandis - R. Paré, Intercategories: a framework for three dimensional category theory, J. Pure Appl. Algebra 221 (2017), 999--1054.
Online publication (30 August 2016) in pdf. Preprint available at arXiv.

[100] M. Grandis - R. Paré, Intercategories, Theory Appl. Categ. 30 (2015), No. 38, 1215--1255.
Available at TAC.

[99] E. Carletti - M. Grandis, Generalised pushouts, connected colimits and codiscrete groupoids, Cah. Topol. Géom. Diff. Catég. 56 (2015), 232--240.
Available at Cahiers (in: Issue 3, third article).

[98] M. Grandis, Orthodox semigroups and coherence in homological algebra, Southeast Asian Bull. Math. 37 (2013), no. 4, 499--514.
Available at SEAMS Bulletin.

[97] M. Grandis, Adjoints for symmetric cubical categories (On weak cubical categories, III), Cah. Topol. Géom. Diff. Catég., 54 (2013), 91--126.
Available at Cahiers (in: Issue 2, third article).

[96] M. Grandis - G. Janelidze - L. Márki, Non-pointed exactness, radicals, closure operators, J. Aust. Math. Soc. 94 (2013), 348--361.

[95] M. Grandis, Distributive lattices and coherence in homological algebra, Asia Pac. Math. Newsl. 2 no. 4 (2012), 11--16.
Extended preprint (Coherence and distributive lattices in homological algebra): Pubbl. Mat. Univ. Genova, Preprint 595 (2012).
Available in pdf.

[94] M. Grandis - R. Paré, From cubical to globular higher categories, in: Liber Amicorum en l'honneur de M.me A.C. Ehresmann, Diagrammes 67-68 suppl. (2012), 117--148.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 594 (2011). Available in pdf.

[93] M. Grandis, A lax symmetric cubical category associated to a directed space, Cah. Topol. Géom. Diff. Catég. 53 (2012), 115--156.
Available at Cahiers (in: Issue 2, second article).

[92] M. Grandis, Singularities and regular paths (An elementary introduction to smooth homotopy), Cah. Topol. Géom. Diff. Catég. 52 (2011), 45--76.
Available at Cahiers (in: Issue 1, second article)

[91] M. Grandis, Homotopy spectral sequences, J. Homotopy Relat. Struct. 5 (2010), 213--252.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 570 (2009). Available in pdf.

[32a] M. Grandis, On homological algebra, I. Semiexact and homological categories, Dip. Mat. Univ. Genova, Preprint 186 (1991).
Available in a slightly revised version (2009): ps.

[33a] M. Grandis, On homological algebra, II. Homology and satellites, Dip. Mat. Univ. Genova, Preprint 187 (1991).
Available in a slightly revised version (2009): ps.

[34a]. M. Grandis, A categorical approach to exactness in algebraic topology, Rend. Circ. Mat. Palermo 29 (1992), 179--213.
Available in a slightly revised version (2009): ps.

[90] M. Grandis, Limits in symmetric cubical categories (On weak cubical categories, II), Cah. Topol. Géom. Diff. Catég. 50 (2009), 242--272.
Available at Cahiers.

[89] M. Grandis, The role of symmetries in cubical sets and cubical categories (On weak cubical categories, I), Cah. Topol. Géom. Diff. Catég. 50 (2009), 102--143.
Available at Cahiers.

[88] M. Grandis, Cubical cospans and higher cobordisms (Cospans in Algebraic Topology, III), J. Homotopy Relat. Struct. 3 (2008), 273--308.
Available at: JHRS

[87] M. Grandis, Collared cospans, cohomotopy and TQFT (Cospans in Algebraic Topology, II), Theory Appl. Categ. 18 (2007), No. 19, 602--630.
Available at TAC.

[86] M. Grandis - R. Paré, Lax Kan extensions for double categories (On weak double categories, Part IV), Cah. Topol. Géom. Diff. Catég. 48 (2007), 163--199.
Available at Cahiers.

[85] M. Grandis - R. Paré, Kan extensions in double categories (On weak double categories, Part III), Theory Appl. Categ. 20 (2008), No. 8, 152--185.
Available at TAC.

[84] M. Grandis, Higher cospans and weak cubical categories (Cospans in Algebraic Topology, I), Theory Appl. Categ. 18 (2007), No. 12, 321--347.
Available at TAC.

[83] M. Grandis, Directed algebraic topology, categories and higher categories, Appl. Categ. Struct. 15 (2007), 341--353.
Available at APCS. Also available here, in pdf.

[83a] M. Grandis, Preface to a special issue: Directed Algebraic Topology and Category Theory, Appl. Categ. Struct. 15 (2007), 339--340.
Available here, in pdf.

[82] M. Grandis - W. Tholen, Natural weak factorisation systems, Archivum Mathematicum (Brno) 42 (2006), 397--408.
Available in pdf .

[81] M. Grandis, The fundamental weighted category of a weighted space: From directed to weighted algebraic topology, Homology Homotopy Appl. 9 (2007), 221--256.
Available at HHA.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 540 (2006), available in pdf.

[80] M. Grandis, Quotient models of a category up to directed homotopy, Theory Appl. Categ. 16 (2006), No. 26, 709--735.
Available at TAC,

[79] M. Grandis, Categories, norms and weights, J. Homotopy Relat. Struct. 2 (2007), No. 9, 171--186.
Available at JHRS.

[78] M. Grandis, Absolute lax 2-categories, Appl. Categ. Struct. 14 (2006), 191--214.
Available at APCS.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 533 (2005). Available in pdf.

[77] M. Grandis, Lax 2-categories and directed homotopy, Cah. Topol. Géom. Diff. Catég. 47 (2006), 107--128.
Available at Cahiers.

[76] M. Grandis, A few points on Directed Algebraic Topology, "Charles Ehresmann: 100 ans", Amiens 2005, Cah. Topol. Géom. Diff. Catég. 46 (2005), 194--195.
Preprint available in pdf.

[75] M. Grandis, Modelling fundamental 2-categories for directed homotopy, Homology Homotopy Appl. 8 (2006), 31--70.
Available from HHA.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 527 (2005). Available in pdf.

[74] M. Grandis, The shape of a category up to directed homotopy, Theory Appl. Categ. 15 (2005/06), No. 4, 95--146.
Paper available at TAC.

[73] M. Grandis, Preface to a special issue: Homotopy theory, Appl. Categ. Struct. 12 (2004), No.1, 1--2.
Available here, in pdf.

[72] M. Grandis, Inequilogical spaces, directed homology and noncommutative geometry, Homology Homotopy Appl. 6 (2004), 413--437.
Available at HHA.

[71] M. Grandis, Equilogical spaces, homology and noncommutative geometry, Cah. Topol. Géom. Diff. Catég. 46 (2005), 53--80.
Available at Cahiers.

[70] M. Grandis, Normed combinatorial homology and noncommutative tori, Theory Appl. Categ. 13 (2004), No. 7, 114--128.
Available at TAC,

[69] M. Grandis, Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology), Math. Proc. Cambridge Philos. Soc. 138 (2005), 233--262.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 480 (May 2003). Revised version: February 04. Available in pdf.

[68] M. Grandis - R. Paré, Adjoints for double categories, Cah. Topol. Géom. Diff. Catég. 45 (2004) 193--240.
Available at Cahiers.

[67]. F. Borceux - M. Grandis, Jordan-Holder, modularity and distributivity in non-commutative algebra, J. Pure Appl. Algebra 208 (2007), 665--689.
Available online 17 April 2006: http://dx.doi.org/10.1016/j.jpaa.2006.03.004
Preprint: Pubbl. Mat. Univ. Genova, Preprint 474 (Feb 2003). Available in dvi and ps.

[25a]. M. Grandis, Weakly exact categories and their relations, December 2002.
Abstract. Available in pdf.
[Slightly revised version of: Weakly exact categories and their relations, Pubbl. Mat. Univ. Genova 20 (1987)].

[66]. M. Grandis, Combinatorial homology in a perspective of image analysis, Georg. Math. J. 10 (2003), 77--98.
Available in pdf.

[65] M. Grandis - G. Janelidze, Galois theory of simplicial complexes, Topology Appl. 132 (2003), 281--289.
Available in pdf.

[64] M. Grandis - L. Mauri, Cubical sets and their site, Theory Appl. Categ. 11 (2003), No. 8, 185--211 (electronic).
Available in pdf

[63] M. Grandis - E. Vitale, A higher dimensional homotopy sequence, Homology Homotopy Appl. 4 (2002), 59--69.
Available at HHA.

[62] M. Grandis, Higher fundamental groupoids for spaces, Topology Appl. 129 (2003), 281--299.
Preprint: Pubbl. Mat. Univ. Genova, Preprint 447 (Jan 2002), 17 p.
Abstract. Available in pdf.

[60] M. Grandis, Directed homotopy theory, I. The fundamental category, Cah. Topol. Géom. Diff. Catég. 44 (2003), 281--316.
Available at Cahiers,

[59] M. Grandis, Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency,
Homology Homotopy Appl. 5 (2003), No. 2, 211--231.
Available at HHA.

[58] M. Grandis, On the monad of proper factorisation systems in categories, J. Pure Appl. Algebra 171 (2002) 17--26.
Preprint: available in pdf.

[57] M. Grandis, A note on exactness and stability in homotopical algebra, Theory Appl. Categ. 9 (2001), No. 2, 17--42.
Available at TAC.

[56] M. Grandis, Higher fundamental functors for simplicial sets, Cah. Topol. Géom. Diff. Catég. 42 (2001), 101--136.
Available at Cahiers.

[55] M. Grandis, Finite sets and symmetric simplicial sets, Theory Appl. Categ. 8 (2001), No. 8, 244--252.
Available at TAC.

[53] M. Grandis, An intrinsic homotopy theory for simplicial complexes, with applications to image analysis,
Appl. Categ. Structures 10 (2002), 99--155.
Preprint: available in pdf.

[51] M. Grandis, Weak subobjects and the epi-monic completion of a category, J. Pure Appl. Algebra 154 (2000), 193--212.
Preprint: available in pdf.

[50] M. Grandis - J. MacDonald, Homotopy structures for algebras over a monad, Appl. Categ. Structures 7 (1999), 227--260.
Preprint: available in pdf.

[49] M. Grandis - R. Paré, Limits in double categories, Cah. Topol. Géom. Diff. Catég. 40 (1999), 162--220.
Available at Cahiers.

[48] M. Grandis, On the homotopy structure of strongly homotopy associative algebras, J. Pure Appl. Algebra 134 (1999), 15--81.

[47] M. Grandis, Weak subobjects and weak limits in categories and homotopy categories, Cah. Topol. Géom. Diff. Catég. 38 (1997), 301--326.
Available at Cahiers.

[46] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures 5 (1997), 363--413.
Preprint: available in pdf.

[45] A. Carboni - M. Grandis, Categories of projective spaces, J. Pure Appl. Algebra 110 (1996), 241--258.

[44] M. Grandis, Simplicial homotopical algebra and satellites, Appl. Categ. Structures 5 (1997), 75--97.

[43] M. Grandis, Cubical homotopical algebra and cochain algebras, Ann. Mat. Pura Appl. 170 (1996) 147--186.

[42] M. Grandis, Homotopical algebra and triangulated categories, Math. Proc. Cambridge Philos. Soc. 118 (1995), 259--295.

[41] M. Grandis, Cubical monads and their symmetries, in: Proc. of the Eleventh Intern. Conf. on Topology, Trieste 1993, Rend. Ist. Mat. Univ. Trieste, 25 (1993), 223--262.
Available at the Journal: pdf.

[40] M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ. Structures 2 (1994), 351--406.

[39] M. Grandis, A note on stability in homotopical algebra, Seminarberichte Fachb. Math. (FernUniv. Hagen) 46 (1993), 84--91.

[38] M. Grandis, Homological algebra in non abelian settings, Unpublished, 1992.

[37] M. Grandis, On the categorical foundations of homological and homotopical algebra, Cah. Topol. Géom. Diff. Catég. 33 (1992), 135--175.
Available at Cahiers.

[36] M. Grandis, Homotopical algebra: a two-dimensional categorical setting, Dip. Mat. Univ. Genova, Preprint 191 (1991), 1--50.

[35] M. Grandis, Fractions for exact categories, Rend. Accad. Naz. Sci. XL Mem. Mat. 16 (1992), 21--38.

[34] M. Grandis, A categorical approach to exactness in algebraic topology, in: Atti del V Convegno Nazionale di Topologia, Lecce-Otranto 1990, Rend. Circ. Mat. Palermo 29 (1992), 179--213.
Preprint available in ps.

[33] M. Grandis, On homological algebra, II. Homology and satellites, Dip. Mat. Univ. Genova, Preprint 187 (1991), 1--39.

[32] M. Grandis, On homological algebra, I. Semiexact and homological categories, Dip. Mat. Univ. Genova, Preprint 186 (1991), 1--45.

[31] M. Grandis, Cohesive categories and measurable operators, Rend. Accad. Naz. Sci. XL Mem. Mat. 14 (1990), 195--234.

[30] M. Grandis, Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 (1990), 199--244.
Available in a slightly revised version of the Preprint, in pdf.

[29] M. Grandis, Manifolds as enriched categories, in: Categorical Topology, Prague 1988, pp.358--368, World Scientific 1989.

[28] R. Betti - M. Grandis, Complete theories in 2-categories, Cah. Topol. Géom. Diff. Catég. 29 (1988), 9--57.
Available at Cahiers.

[27] M. Grandis, A proof for the universal exact system, Dip. Mat. Univ. Genova, Preprint 46 (1988), 1--26.

[26] M. Grandis, Distributive homological algebra: the universal model for the exact system and the exact couple, Boll. Un. Mat. Ital. 2-B (1988), 613--640.

[25] M. Grandis, Weakly exact categories and their relations, Dip. Mat. Univ. Genova 20 (1987), 1--75.

[24] M. Grandis, Convergence in homological algebra, Rend. Accad. Naz. Sci. XL, Mem. Mat. 11 (1987), 205--236.

[23] M. Grandis, The running knot theorem for idempotent categories, Boll. Un. Mat. Ital. 4-A (1985), 279--286.

[22] M. Grandis, On distributive homological algebra, III. Homological theories, Cah. Topol. Géom. Diff. Catég. 26 (1985), 169--213.
Available at Cahiers.

[21] M. Grandis, On distributive homological algebra, II. Theories and models, Cah. Topol. Géom. Diff. Catég. 25 (1984), 353--379.
Available at Cahiers.

[20] M. Grandis, On distributive homological algebra, I. RE-categories, Cah. Topol. Géom. Diff. Catég. 25 (1984), 259--301.
Available at Cahiers.

[19] M. Grandis, Concrete representations for inverse and distributive exact categories, Rend. Accad. Naz. Sci. XL, Mem. Mat. 8 (1984), 99--120.

[18] M. Grandis, Transfer functors and projective spaces, Math. Nachr. 118 (1984), 147--165.

[17] M. Grandis, Canonical models in homological algebra, Reports, Genova 1982.

[16] M. Grandis, Sous-quotients et relations induites dans les catégories exactes, Cahiers Top. Geom. Diff. 22(1981), 231--238.
Available at Cahiers.

[15] M. Grandis, Zeeman diagrams for homological systems, Rapp. Sci. Ist. Mat. Univ. Genova 102 (1981).

[14] M. Grandis, Some categories for Zeeman diagrams, Boll. Un. Mat. Ital. 17-B (1979), 1111--1133.

[13] M. Grandis, Distributive unions in semilattices and inverse symmetrizations, Riv. Mat. Univ. Parma 6 (1980), 363--378

[12] M. Grandis, Exact categories and orthodox symmetrizations (Orthodox symmetrizations, 3), Boll. Un. Mat. Ital. 16-B (1979), 178--195.

[11] M. Grandis, Exact categories and distributive lattices (Orthodox symmetrizations, 2), Ann. Mat. Pura Appl. 118 (1978), 325--341.

[10] M. Grandis, Quaternary categories having orthodox symmetrizations (Orthodox symmetrizations, 1), Boll. Un. Mat. Ital. 14-B (1977), 605--629.

[9] M. Grandis, Quasi-inverse involution semigroups and categories (Orthodox categories, 4), Boll. Un. Mat. Ital. 14-B (1977), 320--339.

[8] M. Grandis, Induction in orthodox involution categories (Orthodox categories, 3), Ann. Mat. Pura Appl. 116 (1978), 87--99.

[7] M. Grandis, Regular and orthodox involution categories (Orthodox categories, 2), Boll. Un. Mat. Ital. 14-A (1977), 38--48.

[6] M. Grandis, Canonical preorder and congruence in orthodox semigroups and categories (Orthodox categories, 1), Boll. Un. Mat. Ital. 13-B (1976), 634--650.

[5] M. Grandis, Symétrisations de categories et factorisations quaternaires, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. 14 sez. 1 (1977), 133--207.

[4] M. Grandis, Symétrisations de catégories, I. Généralités, Rend. Sem. Mat. Univ. Padova 54 (1975), 271--310.
Available at Numdam, in pdf.

[3] M. Grandis, I subquozienti nelle categorie abeliane, Rend. Sem. Mat. Univ. Padova 43 (1970), 63--97.
Available at Numdam, in pdf.

[2] M. Grandis, Il sistema spettrale di un complesso multiplo, Rend. Sem. Mat. Univ. Padova 40 (1968), 252--298.
Available at Numdam, in pdf.

[1] M. Grandis, Spazi con operatori e applicazioni al problema di Knaster, Rend. Sem. Mat. Univ. Padova 38 (1967), 258--286.
Available at Numdam, in pdf.