Zurab Janelidze's Blog

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Mathematics Papers

Published

  1. Z. Janelidze, Characterization of pointed varieties of universal algebras with normal projections, Theory and Applications of Categories 11, 2003, 212-214
  2. Z. Janelidze, Varieties of universal algebras with normal local projections, Georgian Mathematical Journal 11, 2004, 93-98
  3. Z. Janelidze, Subtractive categories, Applied Categorical Structures 13, 2005, 343-350
  4. Z. Janelidze, Closedness properties of internal relations I: A unified approach to Mal’tsev, unital and subtractive categories, Theory and Applications of Categories 16, 2006, 236-261
  5. Z. Janelidze, Closedness properties of internal relations II: Bourn localization, Theory and Applications of Categories 16, 2006, 262-282
  6. Z. Janelidze, Closedness properties of internal relations IV: Expressing additivity of a category via subtractivity, Journal of Homotopy and Related Structures 1, 2006, 219-227
  7. Z. Janelidze, Closedness properties of internal relations III: Pointed protomodular categories, Applied Categorical Structures 15, No. 3, 2007, 325-338
  8. Z. Janelidze, Closedness properties of internal relations V: Linear Mal’tsev conditions, Algebra Universalis 58, 2008, 105-117
  9. D. Bourn and Z. Janelidze, Approximate Mal’tsev operations, Theory and Applications of Categories 21, 2008, 152-171
  10. Z. Janelidze, Cover relations on categories, Applied Categorical Structures 17, 2009, 351-371
  11. D. Bourn and Z. Janelidze, Subtractive categories and extended subtractions, Applied Categorical Structures 17, 2009, 317-343
  12. D. Bourn and Z. Janelidze, Pointed protomodularity via natural imaginary subtractions, Journal of Pure and Applied Algebra 213, 2009, 1835-1851
  13. Z. Janelidze, Closedness properties of internal relations VI: Approximate operations, Cahiers de Topologie et Géométrie Différentielle Catégoriques 50, 2009, 298-319
  14. Z. Janelidze, The pointed subobject functor, 3x3 lemmas, and subtractivity of spans, Theory and Applications of Categories 23, 2010, 221-242
  15. Z. Janelidze and A. Ursini, Split short five lemma for clots and subtractive categories, Applied Categorical Structures 19, 2011, 233-255
  16. D. Bourn and Z. Janelidze, Categorical (binary) difference terms and protomodularity, Algebra Universalis 66, 2011, 277-316
  17. Z. Janelidze and N. Martins-Ferreira, Weakly Mal’tsev categories and strong relations, Theory and Applications of Categories 27, 2012, 65-79
  18. M. Gran, Z. Janelidze, D. Rodelo, and A. Ursini, Symmetry of regular diamonds, the Goursat property, and subtractivity, Theory and Applications of Categories 27, 2012, 80-96
  19. M. Gran, Z. Janelidze, and A. Ursini, A good theory of ideals in regular multi-pointed categories, Journal of Pure and Applied Algebra 216, 2012, 1905-1919
  20. M. Gran, Z. Janelidze, and D. Rodelo, 3x3 lemma for star-exact sequences, Homology, Homotopy and Applications 14(2), 2012, 1-22
  21. Z. Janelidze, An axiomatic survey of diagram lemmas for non-abelian group-like structures, Journal of Algebra 370, 2012, 387-401
  22. D. Rodelo, Z. Janelidze, and T. Van der Linden, Hagemann’s theorem for regular categories, Journal of Homotopy and Related Structures 9, 2014, 55-66
  23. Z. Janelidze, On the Form of Subobjects in Semi-Abelian and Regular Protomodular Categories, Applied Categorical Structures 22, 2014, 755-766
  24. M. Gran and Z. Janelidze, Star-regularity and regular completions, Journal of Pure and Applied Algebra 218, 2014, 1771-1782
  25. Z. Janelidze and T. Weighill, Duality in non-abelian algebra I. From cover relations to grandis ex2-categories, Theory and Applications of Categories 29, 2014, 315-331
  26. D. Bourn and Z. Janelidze, A note on the abelianization functor, Communications in Algebra 44, 2016, 2009-2033
  27. Z. Janelidze and T. Weighill, Duality in non-abelian algebra II. From Isbell bicategories to Grandis exact categories, Journal of Homotopy and Related Structures 11, 2016, 553-570
  28. Z. Janelidze, Duality for diagram chasing a la Mac Lane in non-abelian categories, Homology, Homotopy and Applications 18, 2016, 85-106
  29. Z. Janelidze and T. Weighill, Duality in non-abelian algebra III. Normal categories and 0-regular varieties, Algebra Universalis 77, 2017, 1-28
  30. Z. Janelidze and N. Martins-Ferreira, Involution-rigidness – a new exactness property, and its weak version, Journal of Algebra and Its Applications 16, 2017, 1750074
  31. Z. Janelidze and E. Vitale, Snail lemma in a pointed regular category, Journal of Pure and Applied Algebra 221, 2017, 135-143
  32. M. Duckerts-Antoine, M. Gran and Z. Janelidze, Epireflective subcategories via epi-closure operators, Theory and Applications of Categories 32, 2017, 526-546
  33. A. Goswami and Z. Janelidze, On the structure of zero morphisms in a quasi-pointed category, Applied Categorical Structures 25, 2017, 1037-1043
  34. Z. Janelidze and A. M. Abdalla, An order-theoretic perspective on categorial closure operators, Quaestiones Mathematicae 41, 2018, 529-539
  35. A. Goswami and Z. Janelidze, Duality in non-abelian algebra IV. Duality for groups and a universal isomorphism theorem, Advances in Mathematics 349, 2019, 781-812
  36. M. Hoefnagel, Z. Janelidze, and D. Rodelo, On difunctionality of class relations, Algebra Universalis 81, Article 19, 2020 (15 pages)
  37. P.-A. Jacqmin and Z. Janelidze, On stability of exactness properties under the pro-completion, Advances of Mathematics 377, 2021, 107484 (55 pages)
  38. P.-A. Jacqmin and Z. Janelidze, On linear exactness properties, Journal of Algebra 583, 2021, 38-88.
  39. Z. Janelidze, I. van der Berg, A Dedekind-style axiomatization and the corresponding universal property of an ordinal number system, The Journal of Symbolic Logic 87, 2022, 1396-1418 
  40. M. Hoefnagel, P.-A. Jacqmin, and Z. Janelidze, The matrix taxonomy of finitely complete categories, Theory and Applications of Categories 38, 2022, 737-790
  41. Z. Janelidze, H. Prodinger, and F. van Niekerk, Combinatorics arising from lax colimits of posets, Order (in press, available online), 2023 (29 pages)

Submitted for Publication

  1. M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze, and E. van der Walt, On binary matrix properties, submitted for publication in 2021
  2. K. Dayaram, A. Goswami, and Z. Janelidze, Duality in non-abelian algebra V. Homological diagram lemmas, submitted in 2023
  3. Z. Janelidze and F. K. van Niekerk, Every topos has an optimal noetherian form, submitted for publication in 2023

In Preparation

  1. L. Marki and Z. Janelidze, Formal radical theory, work in progress since 2015
  2. Z. Janelidze, F. K. van Niekerk and J. Viljoen, On the endomatch index of a digraph, in preparation since 2020
  3. K. Dayaram, A. Goswami, and Z. Janelidze, Formal analysis of Yoneda-Quillen exact categories, work in progress since 2021
  4. K. Dayaram, A. Goswami, and Z. Janelidze, A survey of the butterfly lemma, work in progress since 2021
  5. T. Apostolos, K. Dayaram, P. P. Ghosh and Z. Janelidze, Understanding canonical extensions, work in progress since 2022
  6. D. Baboolal, R. Ferguson, Z. Janelidze, P. Pillay, C. Rathilal, and I. van der Berg, A note on the axioms for the diameter of a frame, work in progress since 2022
  7. R. Benjamin, Z. Janelidze, G. Joubert and F. Schulz, Ranked monoids, work in progress since 2022
  8. K. Dayaram, Z. Janelidze, G. Joubert, Cerene Rathilal, Measure detecting maps, work in progress since 2022
  9. R. Ferguson, M. Hoefnagel, Z. Janelidze, C. Msipha, E. Theart, Extensivity for sum structures, work in progress since 2022
  10. R. Ferguson, M. Hoefnagel, Z. Janelidze, C. Msipha, E. Theart, Some remarks on the canonical morphism from the sum to the product, work in progress since 2022
  11. A. Goswami, M. Hoenselaar, Z. Janelidze, and I. van der Berg, Relative lower topology, work in progress since 2022
  12. Z. Janelidze, S. Marques, and D. Moore, On the category of near-vector space, work in progress since 2022


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