Matrix taxonomy and Bourn localization

DOI10.1007/s10485-022-09692-yOpenAlexW4296961657WikidataQ114744375 ScholiaQ114744375MaRDI QIDQ2105680

Michael Hoefnagel, Pierre-Alain Jacqmin

Publication date: 8 December 2022

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.09509

zbMATH Keywords

Mal'tsev categoryfibration of pointsunital categorymatrix propertyarithmetical categoryBourn localization

Mathematics Subject Classification ID

Mechanization of proofs and logical operations (03B35) Equational logic, Mal'tsev conditions (08B05) Epimorphisms, monomorphisms, special classes of morphisms, null morphisms (18A20) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Categories of algebras (08C05) Embedding theorems, universal categories (18B15) Categoricity and completeness of theories (03C35) Formalization of mathematics in connection with theorem provers (68V20) Computer assisted proofs of proofs-by-exhaustion type (68V05) Protomodular categories, semi-abelian categories, Mal'tsev categories (18E13) Computational methods for problems pertaining to category theory (18-08)

Cites Work

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• Diagram chasing in Mal'cev categories
• Subtractive categories
• Arithmetical categories and commutator theory
• Mal'cev categories and fibration of pointed objects
• Anticommutativity and the triangular lemma
• Facets of congruence distributivity in Goursat categories
• Characterizations of majority categories
• Exact categories and categories of sheaves
• Mal'tsev objects, $R_1$-spaces and ultrametric spaces
• Majority categories
• The matrix taxonomy of finitely complete categories
• Products and coequalizers in pointed categories

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