Year: 2019
Type: preprint
Abstract: In universal algebra, it is well known that varieties admitting a majority term admit several Mal'tsev-type characterizations. The main aim of this paper is to establish categorical counterparts of some of these characterizations for regular categories. We prove a categorical version of Bergman's Double-projection Theorem: a regular category is a majority category if and only if every subobject $S$ of a finite product $A_1 \times A_2 \times \cdots \times A_n$ is uniquely determined by its two-fold projections. We also establish a categorical counterpart of the Pairwise Chinese Remainder Theorem for algebras, and characterize regular majority categories by the classical congruence equation $α\cap (β\circ γ) = (α\cap β) \circ (α\cap γ)$ due to A.F.~Pixley.
Source: arXiv (Cornell University)
Author: Hoefnagel, Michael
Institution: Stellenbosch University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2955850484