Duality for diagram chasing a la Mac Lane in non-abelian categories

Journal article
Z. Janelidze
Homology, Homotopy and Applications (to appear)
Publication year: 2016

Semi-abelian forms

Conference talk
Z. Janelidze and A. Goswami
2nd Workshop on Mathematical Structures, Stellenbosch (South Africa) 2015
Publication year: 2015

On the theory of radical theories

Conference talkInvited talk
Z. Janelidze and L. Márki
3rd Workshop on Categorical Algebra, Gargnano (Italy) 2015
Publication year: 2015

On a symmetric proof of the non-abelian snake lemma

Conference talk
Z. Janelidze
Category Theory 2015, Aveiro (Portugal) 2015
Publication year: 2015

Modularity implies restricted permutability

Conference talk
Z. Janelidze and D. Rodelo
Congress of the South African Mathematical Society, Johannesburg (South Africa) 2015
Publication year: 2015

Involution rigidness — a new exactness property, and its weak version

Journal article
Z. Janelidze and N. Martins-Ferreira
Submitted for publication
Publication year: 2015

Groups and duality

Conference talk
Z. Janelidze
Congress of the Georgian Mathematical Society, Batumi (Georgia) 2015
Publication year: 2015

Formal radical theories

Conference talkInvited talk
Z. Janelidze and L. Márki
International Conference on Radicals, Rings, Near-rings and other algebraic structures, Abbey Vorau (Austria) 2015
Publication year: 2015

Duality in non-abelian algebra III. From Isbell bicategories to Grandis exact categories

Journal article
Z. Janelidze and T. Weighill
Submitted for publication (available as CMS preprint)
Publication year: 2015

Duality in non-abelian algebra II. From Isbell bicategories to Grandis exact categories

Journal article
Z. Janelidze and T. Weighill
Submitted for publication (available as a CMS preprint)
Publication year: 2015

A self-dual axiomatic context for homomorphism theorems

Conference talk
Z. Janelidze
Topology, Analysis, Algebra and Geometry, North-West University (South Africa) 2015
Publication year: 2015

A note on the abelianisation functor

Journal article
D. Bourn and Z. Janelidze
Communications in Algebra (to appear)
Publication year: 2015

Subobject chasing revisited

Conference talk
Z. Janelidze
Category Theory 2014, University of Cambridge (UK) 2014
Publication year: 2014

Star-regularity and regular completions

Journal article
M. Gran and Z. Janelidze
Journal of Pure and Applied Algebra 218, 2014, 1771-1782
Publication year: 2014

Projective structured categories

Conference talk
Z. Janelidze
Congress of South African Mathematical Society, Johannesburg (South Africa) 2014
Publication year: 2014

On the form of subobjects in semi-abelian and regular protomodular categories

Journal article
Z. Janelidze
Applied Categorical Structures 22, 2014, 755-766
Publication year: 2014

Introduction to formal closure operators

Conference talk
Z. Janelidze
Seminar dedicated to the 60th birthday of C. Gilmour, Cape Town (South Africa) 2014
Publication year: 2014

Hagemann's theorem for regular categories

Journal article
D. Rodelo, Z. Janelidze, and T. Van der Linden
Journal of Homotopy and Related Structures 9, 2014, 55-66
Publication year: 2014

Duality in non-abelian algebra I. From cover relations to Grandis ex2-categories

Journal article
Z. Janelidze and T. Weighill
Theory and Applications of Categories 29, 2014, 315-331
Publication year: 2014

Towards geometric universal algebra via topological functors

Conference talk
Z. Janelidze
South African Category Theory Day 2, University of Cape Town (South Africa), 2013
Publication year: 2013

Towards a systematic study of methods for generalizing results from the context of varieties of universal algebra to the context of abstract categories

Conference talkInvited talk
Z. Janelidze
1st Workshop on Categorical Methods in Non-Abelian Algebra, Coimbra (Portugal), 2013
Publication year: 2013

Homological Algebra via Bifibrations

Conference talk
Z. Janelidze (joint work with T. Van der Linden)
Séminaire Itinérant de Catégories, Louvain-la-Neuve (Belgium), 24 May 2013
Publication year: 2013

Cover relations on categories: old and new examples

Conference talk
Z. Janelidze
South African Category Theory Day 1, Stellenbosch University (South Africa), 2013
Publication year: 2013

Bifibrational duality for groups and in general categories

Conference talkInvited talk
Z. Janelidze
Category Theory 2013, Sydney (Australia), July 2013
Publication year: 2013

A new Mal'tsev condition which holds for rings, does not hold for groups, and implies permutability of congruences

Conference talk
Z. Janelidze
56th Congress of South African Mathematical Society, Pietermaritzburg (South Africa), 2013
Publication year: 2013

Weakly Mal'tsev categories and strong relations

Journal article
Z. Janelidze and N. Martins-Ferreira
Theory and Applications of Categories 27, 2012, 65-79
Publication year: 2012

Symmetry of regular diamonds, the Goursat property, and subtractivity

Journal article
M. Gran, Z. Janelidze, D. Rodelo, and A. Ursini
Theory and Applications of Categories 27, 2012, 80-96
Publication year: 2012

Subtraction and subtractivity

Conference talk
Z. Janelidze
55th Annual Congress of South African Mathematical Society (South Africa), 2012
Publication year: 2012

Formal duality in semi-abelian categories

Conference talk
Z. Janelidze
Workshop on Category Theory in honor of George Janelidze, on the occasion of his 60'th birthday, Coimbra (Portugal), 2012
Publication year: 2012

Formal duality for groups

Seminar talk
Z. Janelidze
A. Razmadze Mathematical Institute, Tbilisi (Georgia), 15 Jule 2012
Publication year: 2012

An axiomatic survey of diagram lemmas for non-abelian group-like structures

Journal article
Z. Janelidze
Journal of Algebra 370, 2012, 387-401
Publication year: 2012

A good theory of ideals in regular multi-pointed categories

Journal article
M. Gran, Z. Janelidze, and A. Ursini
Journal of Pure and Applied Algebra 216, 2012, 1905–1919
Publication year: 2012

$3\times 3$ lemma for star-exact sequences

Journal article
M. Gran, Z. Janelidze, and D. Rodelo
Homology, Homotopy and Applications 14, 2012, 1-22
Publication year: 2012

Split short five lemma for clots and subtractive categories

Journal article
Z. Janelidze and A. Ursini
Applied Categorical Structures 19, 2011, 233-255
Publication year: 2011

On the $3\times 3$ lemma

Conference talkInvited talk
Diana Rodelo (joint work with M. Gran and Z. Janelidze)
2nd Workshop on Categorical Algebra: Recent developments and future perspectives, Gargnano (Italy), 2011
Publication year: 2011

Fibred algebraic theories

Conference talkInvited talk
Z. Janelidze
2nd Workshop on Categorical Algebra: Recent developments and future perspectives, Gargnano (Italy), 2011
Publication year: 2011

Categorical (binary) difference terms and protomodularity

Journal article
D. Bourn and Z. Janelidze
Algebra Universalis 66, 2011, 277-316
Publication year: 2011

Une bonne théorie des idéaux dans les catégories régulières

Conference talk
M. Gran (joint work with Z. Janelidze and A. Ursini)
Séminaire Itinérant de Catégories, Paris (France), 2010
Publication year: 2010

The pointed subobject functor, 3x3 lemmas, and subtractivity of spans

Journal article
Z. Janelidze
Theory and Applications of Categories 23, 2010, 221-242
Publication year: 2010

The derived closure-interior operator pair

Conference talk
Z. Janelidze
(Mini-) Conference in Universal Algebra and its connections with Category Theory, Logic, Lattice Theory and Topology, Stellenbosch University (South Africa), 9 March 2010
Publication year: 2010

The architecture of ideal determined categories

Conference talk
Z. Janelidze
Séminaire Itinérant de Catégories, Calais (France), 5 November 2010
Publication year: 2010

The algebra of a general category

Seminar talk
Z. Janelidze
A. Razmadze Mathematical Institute, Tbilisi (Georgia), 30 June 2010
Publication year: 2010

Subtractivity up to a class of morphisms

Conference talk
Z. Janelidze (joint work with D. Bourn)
Seminar in Category Theory, Stellenbosch University (South Africa), 4 February 2010
Publication year: 2010

Categorical terms for congruence-modularity

Conference talk
Z. Janelidze
Special session on Universal Algebra, American Mathematical Society Sectional Meeting, 10-11 April St Paul (USA), 2010
Publication year: 2010

Categorical algebra via difference terms

Conference talk
Z. Janelidze (joint work with D. Bourn)
(Mini-) Conference in Universal Algebra and its connections with Category Theory, Logic, Lattice Theory and Topology, Stellenbosch University (South Africa), 9 March 2010
Publication year: 2010

Algebraic importance of "modus ponens"

Conference talk
Z. Janelidze (joint work with D. Bourn)
Logic and Algebra Day, Stellenbosch University (South Africa), 2 October 2010
Publication year: 2010

Algebraic aspects of categories with finite colimits

Conference talk
Z. Janelidze (joint work with D. Bourn)
Séminaire Itinérant de Catégories, Amiens (France), 5 June 2010
Publication year: 2010

Une alternative à un théorème de plongement pour les catégories protomodulaires

Conference talk
D. Bourn (joint work with Z. Janelidze)
Séminaire Itinérant de Catégories, Paris (France), 2009
Publication year: 2009

The pointed subobject functor and subtractive spans

Conference talk
Z. Janelidze
International Workshop in Categorical Algebra, Stellenbosch University (South Africa), 2009
Publication year: 2009

The algebra of categorical subtractivity

Invited talkSeminar talk
Z. Janelidze
University of Siena, Siena (Italy), 2009
Publication year: 2009

Subtractive categories and extended subtractions

Journal article
D. Bourn and Z. Janelidze
Applied Categorical Structures 17, 2009, 317-343
Publication year: 2009

Pointed protomodularity via natural imaginary subtractions

Journal article
D. Bourn and Z. Janelidze
Journal of Pure and Applied Algebra 213, 2009, 1835-1851
Publication year: 2009

On the category of near vector spaces

Seminar talk
Z. Janelidze
Algebra seminar, Stellenbosch University (South Africa), 2009
Publication year: 2009

Making subtraction homomorphic in groups, rings, and other similar structures

Seminar talk
Z. Janelidze
Algebra seminar, Stellenbosch University (South Africa), 2009
Publication year: 2009

D. Bourn’s homological lemmas in normal categories

Conference talk
Z. Janelidze
89th Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve (Belgium), 2009
Publication year: 2009

Cover relations on categories

Journal article
Z. Janelidze
Applied Categorical Structures 17, 2009, 351-371
Publication year: 2009

Closure operators and regular logic

Seminar talk
Z. Janelidze
Lattice theory and topology seminar, Stellenbosch University (South Africa), 2009
Publication year: 2009

Closedness properties of internal relations VI: Approximate operations

Journal article
Z. Janelidze
Cahiers de Topologie et Géométrie Différentielle Catégoriques 50, 2009, 298-319
Publication year: 2009

The codiagonal extended category structure of a protomodular category with finite coproducts

Conference talkInvited talk
Z. Janelidze (joint work with D. Bourn)
Categories in Algebra, Geometry and Logic (A tribute to the work of Francis Borceux and Dominique Bourn on the occasion of their sixtieth birthday), Royal Flemish Academy of Belgium for Sciences and the Arts, Brussels (Belgium), 2008
Publication year: 2008

Subtractivity in Categorical Algebra

Conference talk
Z. Janelidze
Category Theory 2008, Calais (France), 2008
Publication year: 2008

Extended subtraction and protomodularity

Conference talk
D. Bourn (joint work with Z. Janelidze)
Max Kelly Conference in Category Theory, Cape Town (South Africa), 2008
Publication year: 2008

Closedness properties of internal relations V: Linear Mal’tsev conditions

Journal article
Z. Janelidze
Algebra Universalis 58, 2008, 105-117
Publication year: 2008

Closedness properties of internal relations and approximate operations

Conference talk
Z. Janelidze
Max Kelly Conference in Category Theory, Cape Town (South Africa), 2008
Publication year: 2008

Approximate Mal'tsev operations

Journal article
D. Bourn and Z. Janelidze
Theory and Applications of Categories 21, 2008, 152–171
Publication year: 2008

Algebraic syntax in general categories

Seminar talk
Z. Janelidze (joint work with D. Bourn)
Colloquium Talk, Stellenbosch University (South Africa), 2008
Publication year: 2008

Cover relations: A unified setting for certain factorization systems and certain monoidal structures

Seminar talk
Z. Janelidze
Topology group seminar, University of Cape Town (South Africa), 2007
Publication year: 2007

Cover relations on categories

Conference talk
Z. Janelidze
Category Theory 2007, Algavre (Portugal), 2007
Publication year: 2007

losedness properties of internal relations III: Pointed protomodular categories

Journal article
Z. Janelidze
Applied Categorical Structures 15, 2007, 325-338
Publication year: 2007

Categorical term conditions

Conference talk
Z. Janelidze (joint work with D. Bourn)
Summer School on Contemporary Categorical Methods in Algebra and Topology, Haute-Bodeux (Belgium), 2007
Publication year: 2007

Categorical criteria for solvability of systems of linear equations in rings and more generally in algebraic theories

Conference talk
Z. Janelidze
International Conference on Homology Theories, K-Theory and Homotopy Theory, Tbilisi (Georgia), 2007
Publication year: 2007

Approximate operations in categorical algebra

Conference talk
Z. Janelidze (joint work with D. Bourn)
50th Annual Congress of South African Mathematical Society, Cape Town (South Africa), 2007
Publication year: 2007

Closedness properties of internal relations IV: Expressing additivity of a category via subtractivity

Journal article
Z. Janelidze
Journal of Homotopy and Related Structures 1, 2006, 219-227
Publication year: 2006

Closedness properties of internal relations in universal and categorical algebra

Seminar talk
Z. Janelidze
Topology group seminar, University of Cape Town (South Africa), 2006
Publication year: 2006

Closedness properties of internal relations II: Bourn localization

Journal article
Z. Janelidze
Theory and Applications of Categories 16, 2006, 262-282
Publication year: 2006

Closedness properties of internal relations I: A unified approach to Mal'tsev, unital and subtractive categories

Journal article
Z. Janelidze
Theory and Applications of Categories 16, 2006, 236-261
Publication year: 2006

Characterizations of additive categories via subtractivity

Conference talk
Z. Janelidze
49th Annual Congress of South African Mathematical Society, Bloemfontain (South Africa), 2006
Publication year: 2006

Subtractive categories

Journal article
Z. Janelidze
Applied Categorical Structures 13, 2005, 343-350
Publication year: 2005

Elementary term conditions on varieties of universal algebras

Conference talk
Z. Janelidze
Congress of Georgian Mathematicians, Tbilisi (Georgia), 2005
Publication year: 2005

Varieties of universal algebras with normal local projections

Journal article
Z. Janelidze
Georgian Mathematical Journal 11, 2004, 93-98
Publication year: 2004

New Bourn localization theorems

Conference talk
Z. Janelidze
Algebraic Models of Topological Spaces and Fibrations (Dedicated to the 90th anniversary of George Chogoshvili), Tbilisi (Georgia), 2004
Publication year: 2004

Matrices of derived operators and new localization theorems in categorical algebra

Student conference talk
Z. Janelidze
Georgian State Conference of University Students, Tbilisi (Georgia), 2004
Publication year: 2004

Generalized difunctionality, Pixley categories, and a general Bourn localization theorem

Conference talk
Z. Janelidze
67th Workshop on General Algebra and 19th Conference for Young Algebraists, Potsdam (Germany), 2004
Publication year: 2004

A unified approach to Mal'tsev, unital, and subtractive categories

Seminar talk
Z. Janelidze
Australian category seminar, University of Sydney, Sydney (Australia), 10 March 2004
Publication year: 2004

Subtractivity and normal projections

Conference talk
Z. Janelidze
European Category Theory Meeting, Haute-Bodeux (Belgium), 2003
Publication year: 2003

Subtractive categories

Seminar talk
Z. Janelidze
Australian Category Seminar, Macquarie University, Sydney (Australia), 3 December 2003
Publication year: 2003

Normal projections in Universal Algebra

Conference talk
Z. Janelidze
International Conference on Algebraic and Topological Methods in Non-Classical Logics, Tbilisi (Georgia), 2003
Publication year: 2003

Characterization of pointed varieties of universal algebras with normal projections

Journal article
Z. Janelidze
Theory and Applications of Categories 11, 2003, 212-214
Publication year: 2003

Characterization of pointed varieties of universal algebras with normal projections

Student conference talk
Z. Janelidze
Scientific Conference of Tbilisi State University Students, Tbilisi (Georgia), 2003
Publication year: 2003

Categories with normal local projections

Seminar talk
Z. Janelidze
Australian category seminar, University of Sydney, Sydney (Australia), 10 December 2003
Publication year: 2003

Description of several constructions of higher-dimensional categorical Galois theory

Student conference talk
Z. Janelidze (supervised by G. Janelidze)
Scientific Conference of Tbilisi State University Students, Tbilisi (Georgia), 2002
Publication year: 2002

On the semi-direct product of monoids

Student conference talk
Z. Janelidze (supervised by G. Janelidze)
Scientific Conference of Tbilisi State University Students, Tbilisi (Georgia), 2001
Publication year: 2001

Algebraic models of higher dimensional affine spaces

Student conference talk
Z. Janelidze (supervised by G. Janelidze)
State Scientific Conference of High School Students, Tbilisi (Georgia), 1998
Publication year: 1998