We give two simple generalizations of commutative rings. They form (co)-complete categories, that contain commutative (semi-) rings (e.g. f0; 1g ⊆ [0; 1] ⊆ [0; 1) with the usual multiplication x + y := maxfx; yg). But they also contains … Continue reading Colloquium: Monday, November 20, 4 pm. Speaker: Shai Haran (Technion). Title: “Geometry over F1”.