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Characterizations of Majority Categories
Applied Categorical Structures ( IF 0.6 ) Pub Date : 2019-06-26 , DOI: 10.1007/s10485-019-09571-z Michael Hoefnagel
Applied Categorical Structures ( IF 0.6 ) Pub Date : 2019-06-26 , DOI: 10.1007/s10485-019-09571-z Michael Hoefnagel
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 $$A_1 \times A_2 \times \cdots \times A_n$$ A 1 × A 2 × ⋯ × A n is uniquely determined by its twofold 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 $$\alpha \cap (\beta \circ \gamma ) = (\alpha \cap \beta ) \circ (\alpha \cap \gamma )$$ α ∩ ( β ∘ γ ) = ( α ∩ β ) ∘ ( α ∩ γ ) due to A.F. Pixley.
更新日期：2019-06-26
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