2022/08/19 by Michael Hoefnagel, Hoefnagel, Michael, Pierre-Alain Jacqmin +1
Mathematics · #03C05 #08A55 #08B05 #08C10 (secondary) #18-08 (primary) #18A35 #18C05 #18E08 #18E13 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.09516
openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in general, they can only be stated for regular categories. We study when such a matrix condition implies the Mal'tsev property. Our main results assert that, for both types of matrices, this implication is equivalent to the corresponding implication restricted to the context of varieties of universal algebras.