Jónsson categories
 
 
Description:  In this work we generalise Jónsson's theorem for congruence distributive varieties of universal algebras. The linear Mal'tsev condition extracted from the ternary Jónsson terms give rise to matrix conditions Jn, n ≥ 1. We characterise regular categories C which satisfy (the matrix condition) Jn, for some n ≥ 1, through properties involving equivalence and reflexive relations on a same object in C. These properties on relations then allow us to show that, when C is an n-permutable category, C satisfies Jm, for some m ≥ 1, if and only if C is equivalence distributive. It turns out that regular categories C that satisfy Jn are such that the Trapezoid Lemma holds in C; consequently, every such C is factor permutable.

This is a joint work with Michael Hoefnagel.
Date:  2022-10-18
Start Time:   15:00
Speaker:  Diana Rodelo (CMUC & Univ. Algarve)
Institution:  Univ. do Algarve
Place:  Sala Pedro Nunes, DMUC
Research Groups: -Algebra, Logic and Topology
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Financiado total ou parcialmente pela FCT, Fundação para a Ciência e a Tecnologia, I.P., sob o Financiamento de:
UID/00324/2025 Projeto Estratégico com a referência DOI https://doi.org/10.54499/UID/00324/2025.
https://doi.org/10.54499/UID/PRR/00324/2025     UID/PRR/00324/2025   https://doi.org/10.54499/UID/PRR2/00324/2025   UID/PRR2/00324/2025
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