Geodesic
Weil 2-rigs
Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 382-402

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Among commutative unital semirings (rigs, for short), we call Weil the ones that have a unique homomorphism into the initial algebra. Weil rigs can be thought of as coordinate algebras of spaces with a single point. In the category of additively idempotent rigs (2-rigs, for short) 2 is the initial algebra. We characterize Weil 2-rigs as those that have a unique saturated prime ideal and provide an axiomatization thereof in geometric logic. We further prove that the category of Weil 2-rigs is a co-reflective full subcategory of the category of 2-rigs. Finally, we show that both the varieties of rigs, 2-rigs and integral rigs are generated by finite rigs with a unique homomorphism into 2.
Publié le :
Classification : 16Y60, 03C05
Keywords: Extensive categories, Rigs, Weil algebra 
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Luca Spada; Gavin St. John. Weil 2-rigs. Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 382-402. http://geodesic.mathdoc.fr/item/TAC_2025_43_a11/