On the Naturalness of Mal’tsev Categories

DOI10.1007/978-3-030-66545-6_3zbMath1482.18003arXiv1904.06719OpenAlexW2938585625MaRDI QIDQ5014594

Marino Gran, Pierre-Alain Jacqmin, Dominique Bourn

Publication date: 8 December 2021

Published in: Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.06719

Mathematics Subject Classification ID

Finitary algebras (08A62) Protomodular categories, semi-abelian categories, Mal'tsev categories (18E13)

Related Items (3)

Unnamed Item ⋮ The matrix taxonomy of finitely complete categories ⋮ An Introduction to Regular Categories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new characterisation of Goursat categories
• Central reflections and nilpotency in exact Mal'tsev categories
• Diagram chasing in Mal'cev categories
• The ``closed subgroup theorem for localic herds and pregroupoids
• Subtractive categories
• Baer sums in homological categories
• Representation of categories
• Mal'cev varieties
• Some remarks on Maltsev and Goursat categories
• Galois theory and a general notion of central extension
• A Mal'cev condition for admissible relations
• An embedding theorem for regular Mal'tsev categories
• The 3-by-3 lemma for regular Goursat categories
• Centrality and connectors in Maltsev categories.
• Higher commutator conditions for extensions in Mal'tsev categories
• Internal categories in Mal'cev categories
• Affine categories and naturally Mal'cev categories
• Intrinsic centrality and associated classifying properties
• The denormalized \(3{\times}3\) lemma
• A categorical approach to commutator theory
• Arithmetical categories and commutator theory
• Mal'cev categories and fibration of pointed objects
• The cuboid lemma and Mal'tsev categories
• Higher central extensions in Mal'tsev categories
• On \(n\)-permutable congruences
• Embedding theorems for Janelidze's matrix conditions
• Higher Hopf formulae for homology via Galois theory
• Congruence distributivity in Goursat and Mal'cev categories
• Implication algebras are 3-permutable and 3-distributive
• Beck-Chevalley condition and Goursat categories
• Normal Sections and Direct Product Decompositions
• Goursats Theorem and the Zassenhaus Lemma
• Reflexive Homomorphic Relations
• COMMUTATOR, NILPOTENCY, AND SOLVABILITY IN CATEGORIES
• Relations binaires, fermetures, correspondances de Galois

This page was built for publication: On the Naturalness of Mal’tsev Categories