We extend all known results about transferred model structures on algebraically cofibrant and fibrant objects by working with weak categories. show that for an accessible category there are always Quillen equivalent both the categories of objects. Under additional assumptions, these shown to be left, right or structures. By combining constructions, we each combinatorial is connected, via a chai...

We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse. In this note, an outer billiard table is a compact convex domain in the plane bounded by an oval (closed smooth strictly convex curve) C. Pick a point x outside of C. There are two tangent lines from x to C; choose one of them, say, the right one...