Publications

PREPRINTS

• 54. A. Ardizzoni, C. Menini, P. Saracco, Integrals for Monoid Algebras and Left Adjustable Monoid, work in progress.

• 53. A. Ardizzoni, C. Menini, P. Saracco, Integrals for Bialgebras, preprint. (arxiv:2509.14823)

↪︎ See Saracco's talk at the "European Non-Associative Algebra Seminar"

• 52. A. Ardizzoni, A. Sciandra, The binary product in the 2-category of triangular bialgebras and twisted morphisms, preprint. (arxiv:2506.16469)

• 51. A. Ardizzoni, C. Menini, P. Saracco, On the Hopf envelope of finite-dimensional bialgebras, preprint. (arxiv:2504.05821)

PUBLISHED

• 50. A. Ardizzoni, L. Bottegoni, A. Sciandra, T. Weber, Infinitesimal braidings and pre-Cartier bialgebras, Commun. Contemp. Math., Vol. 27, No. 05, 2450029 (2025).  (doi:10.1142/S0219199724500299) 

↪︎ See Weber's talk at the "North Atlantic Noncommutative Geometry Seminar - 2023"

• 49. A. Ardizzoni, L. Bottegoni, Semiseparable Functors and Conditions up to Retracts, Appl. Categ. Structures, 32, 24 (2024). Open Access. (doi:10.1007/s10485-024-09782-z)

• 48. A. Ardizzoni, L. Bottegoni, Semiseparable Functors, J. Algebra. 638  (2024), 862-917. Open Access.  (doi:10.1016/j.jalgebra.2023.10.007) 

↪︎ See Bottegoni's talk at the "Categories and Companions Symposium - 2021" 

• 47. A. Ardizzoni, I. Goyvaerts, C. Menini, Pre-Rigid Monoidal Categories,  Quaest. Math. 46 (2023), no. 8, 1503-1546. (doi:10.2989/16073606.2022.2112106)

• 46. A. Ardizzoni, I. Goyvaerts, C. Menini, Liftable Pairs of Functors and Initial Objects,  Rend. Circ. Mat. Palermo, II. Ser 72 (2023), 1879–1918.  Open Access. (doi:10.1007/s12215-022-00765-4)

• 45. A. Ardizzoni, L. El Kaoutit, P. Saracco, Toward Differentiation and Integration Between Hopf Algebroids and Lie Algebroids, Publ. Mat., 67 (2023), no. 1, 3-88. (doi:10.5565/PUBLMAT6712301)

• 44. A. Ardizzoni, P. Saracco and D. Ştefan, PBW-Deformations of Graded Rings,  Israel J. Math. 249 (2022), no. 2, 769–856. (doi:10.1007/s11856-022-2325-3)

• 43. A. Ardizzoni, C. Menini, Monadic vs Adjoint Decomposition,  J. Pure Appl. Algebra. Volume 226 (2022), no. 8, Paper No. 106945, 47 pp. (doi:10.1016/j.jpaa.2021.106945)

↪︎ See my talk at the "Category Theory CT20->21" 

• 42. A. Ardizzoni and F. Stumbo, On Indecomposable Ideals Over Some Algebras, Algebr. Represent. Theory 23 (2020), no.4, 1443–1466. (doi:10.1007/s10468-019-09900-9)

• 41. A. Ardizzoni, C. Menini, Heavily Separable Functors, J. Algebra 543 (2020), 170-197. (doi:10.1016/j.jalgebra.2019.10.008)

• 40. A. Ardizzoni, I. Goyvaerts, C. Menini, Restricted Lie algebras via monadic decomposition, Algebr. Represent. Theory 21 (2018), 703–716. (doi:10.1007/s10468-017-9734-8)

• 39.  I. E. Angiono, A. Ardizzoni, and C. Menini, Cohomology and Coquasi-bialgebras in Yetter-Drinfeld Modules, Ann. Sc. Norm. Super. Pisa Cl. Sci (5), Vol. XVII (2017), 609-653. (doi:10.2422/2036-2145.201509_018)

• 38. A. Ardizzoni and L. El Kaoutit, Invertible Bimodules, Miyashita Action in Monoidal Categories and Azumaya Monoids, Nagoya Math. J.. Vol. 225 (2017), p. 1-63. (doi:10.1017/nmj.2016.25)

• 37. A. Ardizzoni, F. Galluzzi and F. Vaccarino, A new family of algebras whose representation schemes are smooth, Ann. Inst. Fourier (Grenoble), Vol. 66 no. 3 (2016), p. 1261-1277. (Paper) (doi:10.5802/aif.3037)

• 36. A. Ardizzoni, L. El Kaoutit and P. Saracco, Functorial Constructions for Non-associative Algebras with Applications to Quasi-bialgebras, J. Algebra,  Vol. 449 (2016), 460-496.(doi:10.1016/j.jalgebra.2015.11.029)

• 35. A. Ardizzoni and C. Menini, Milnor-Moore Categories and Monadic Decomposition, J. Algebra, Vol. 448 (2016), 488-563. (doi:10.1016/j.jalgebra.2015.09.031)

• 34. A. Ardizzoni, M. Beattie and C. Menini, Quantum Lines for Dual Quasi-Bialgebras, Algebr. Represent. Theory, Vol. 18, Issue 1 (2015), 35-64. (doi:10.1007/s10468-014-9478-7) 

• 33. A. Ardizzoni, J. Gómez-Torrecillas and C. Menini, Monadic Decompositions and Classical Lie Theory, Appl. Categor. Struct., Vol. 23, Issue 1 (2015), 93-105. (doi:10.1007/s10485-013-9326-7) 

• 32. A. Ardizzoni and C. Menini, Adjunctions and Braided Objects, J. Algebra Appl. Vol. 13(06) (2014), 1450019 (47 pages). (doi:10.1142/S0219498814500194) 

• 31. A. Ardizzoni, D. Bulacu and C. Menini, Quasi-bialgebra Structures and Torsion-free Abelian Groups, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 56(104) No. 3 (2013), 247-265. 

• 30. A. Ardizzoni, A. Pavarin, Bosonization for Dual Quasi-Bialgebras and Preantipode, J. Algebra, Vol. 390 (2013), 126-159.(doi:10.1016/j.jalgebra.2013.05.014) 

• 29. A. Ardizzoni, L. El Kaoutit and C. Menini, Coendomorphism left bialgebroids, J. Algebra Appl.. Vol. 12(03) (2013), 1250181 (21 pages). (doi:10.1142/S0219498812501812) 

• 28. A. Ardizzoni, A. Pavarin, Preantipodes for Dual Quasi-Bialgebras, Israel J. Math., Vol. 192(1) (2012), 281-295. (doi:10.1007/s11856-012-0024-1) 

• 27. A. Ardizzoni, L. El Kaoutit and C. Menini, Categories of comodules and chain complexes of modules, Internat. J. Math., Vol. 23(10) (2012), 1250109 (36 pages). (doi:10.1142/S0129167X12501091) 

• 26. A. Ardizzoni, On Primitively Generated Braided Bialgebras, Algebr. Represent. Theory, Vol. 15(4) (2012), 639-673. (doi:10.1007/s10468-010-9257-z) 

• 25. A. Ardizzoni, M. Beattie and C. Menini, Gauge Deformations for Hopf Algebras with the Dual Chevalley Property, J. Algebra Appl., Vol. 11(3) (2012), 1250051. (doi:10.1142/S0219498811005798) 

• 24. A. Ardizzoni and C. Menini, Associated Graded Algebras and Coalgebras, Comm. Algebra, Vol. 40(3) (2012), 862-896. (doi:10.1080/00927872.2010.540286) 

• 23. A. Ardizzoni, Universal Enveloping Algebras of PBW Type, Glasg. Math. J., Vol. 54(1) (2012), 9-26. (doi:10.1017/S0017089511000310) 

• 22. A. Ardizzoni, M. Beattie and C. Menini, Cocycle Deformations for Liftings of Quantum Linear Spaces, Comm. Algebra, Vol. 39(12) (2011), 4518-4535. (doi:10.1080/00927872.2011.616430)

• 21. A. Ardizzoni and F. Stumbo, Quadratic Lie Algebras, Comm. Algebra, Vol. 39(8) (2011), 2723-2751. (doi:10.1080/00927872.2010.489917) 

• 20. A. Ardizzoni, On the Combinatorial Rank of a Graded Braided Bialgebra, J. Pure Appl. Algebra, 215 (2011) 2043-2054. (doi:10.1016/j.jpaa.2010.11.014) 

• 19. A. Ardizzoni, A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras, J. Algebra, Vol. 327(1) (2011), 337-365. (doi:10.1016/j.jalgebra.2010.07.031) 

• 18. A. Ardizzoni, M. Beattie and C. Menini, Cocycle Deformations for Hopf Algebras with a Coalgebra Projection, J. Algebra, Vol. 324(4) (2010) 673–705. (doi:10.1016/j.jalgebra.2010.04.027)

• 17. A. Ardizzoni and C. Menini, Small Bialgebras with a Projection: Applications, Comm. Algebra, Vol. 37(8) (2009), 2742-2784. (doi:10.1080/00927870802623419) 

• 16. A. Ardizzoni and C. Menini, Some Remarks on Connected Coalgebras, Algebr. Represent. Theory, Vol. 12 (2009), 235-249.(doi:10.1007/s10468-009-9147-4) 

• 15. A. Ardizzoni, C. Menini and D. Ştefan, Braided Bialgebras of Hecke-type, J. Algebra, Vol. 321 (2009), 847-865. (doi:10.1016/j.jalgebra.2008.11.011) 

• 14. A. Ardizzoni and C. Menini, Braided Bialgebras of Type One, Comm. Algebra, Vol. 36(11) (2008), 4296-4337. (doi:10.1080/00927870802157673 )

• 13. A. Ardizzoni, Wedge Products and Cotensor Coalgebras in Monoidal Categories, Algebr. Represent. Theory, Vol. 11(5) (2008), 461-496. (doi:10.1007/s10468-008-9089-2)

• 12. A. Ardizzoni, Separable Functors and formal smoothness, J. K-theory, Vol. 1 (2008), 535-582. (doi:10.1017/is007011015jkt012) 

• 11. A. Ardizzoni and C. Menini, A categorical proof of a useful result, in "Modules and Comodules" Proceedings of a conference dedicated to Robert Wisbauer. Edited by T. Breziński, J. L. Gómez Pardo, I. Shestakov and P. F. Smith. Trends in Math Vol. XII, Birkhäuser Verlag, Basel, 2008, 31-45.

• 10. A. Ardizzoni, T. Brzeziński and C. Menini, Formally Smooth Bimodules, J. Pure Appl. Algebra, Vol. 212(5) (2008), 1072-1085. (doi:10.1016/j.jpaa.2007.09.004). 

• 9. A. Ardizzoni, G. Böhm and C. Menini, A Schneider type Theorem for Hopf Algebroids, J. Algebra, Vol. 318(1) (2007), 225-269. (doi:10.1016/j.jalgebra.2007.05.017); Corrigendum to ''A Schneider type Theorem for Hopf Algebroids'' [J. Algebra 318 (2007) 225-269], ibidem, Vol. 321(6) (2009), 1786-1796. (doi:10.1016/j.jalgebra.2008.11.040)

• 8. A. Ardizzoni, C. Menini and D. Ştefan, Weak Projections onto a Braided Hopf Algebra, J. Algebra, Vol. 318(1) (2007), 180-201. (doi:10.1016/j.jalgebra.2007.04.009)

• 7. A. Ardizzoni, C. Menini and F. Stumbo, Small Bialgebras with a Projection, J. Algebra, Vol. 314(2) (2007), 613-663. (doi:10.1016/j.jalgebra.2007.04.008) 

• 6. A. Ardizzoni, C. Menini and D. Ştefan, Cotensor Coalgebras in Monoidal Categories, Comm. Algebra, Vol. 35(1) (2007), 25-70. (doi:10.1080/00927870600936856) 

• 5. A. Ardizzoni, The Heyneman-Radford Theorem for Monoidal Categories, J. Algebra, Vol. 308 (2007), 63-72. (doi:10.1016/j.jalgebra.2006.06.006)

• 4. A. Ardizzoni, C. Menini and D. Ştefan, A Monoidal Approach to Splitting Morphisms of Bialgebras, Trans. Amer. Math. Soc., 359 (2007), 991-1044. (doi:10.1090/S0002-9947-06-03902-X) 

• 3. A. Ardizzoni, C. Menini and D. Ştefan, Hochschild Cohomology And ‘Smoothness’ In Monoidal Categories, J. Pure Appl. Algebra, Vol. 208 (2007), 297-330. (doi:10.1016/j.jpaa.2005.12.003).

• 2. A. Ardizzoni, S. Caenepeel, C. Menini and G. Militaru, Naturally Full Functors in nature, Acta Math. Sin. (Engl. Ser.), Vol. 22 (2006), 233-250. (doi:10.1007/s10114-005-0561-1) 

• 1. A. Ardizzoni, The Category of Modules over a Monoidal Category: Abelian or not?, Ann. Univ. Ferrara - Sez. VII - Sc. Mat., Vol. L (2004), 167-185. (doi:10.1007/BF02825349)