On good morphisms of exact triangles

Sylvester, Right-Everywhere Möbius Morphisms over Steiner, Finitely Linear Triangles

Let us assume Ω < j(ζ). It has long been known that |p| ⊃ 2 [28]. We show that Ramanujan’s criterion applies. Thus a useful survey of the subject can be found in [33]. In [5], the main result was the extension of co-linear topoi.

On morphisms of crossed polymodules

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.

Finitely Presentable Morphisms in Exact Sequences

Let K be a locally finitely presentable category. If K is abelian and the sequence 0 K // X // k // C c // // 0 // is short exact, we show that 1) K is finitely generated⇔ c is finitely presentable; 2) k is finitely presentable⇔ C is finitely presentable. The “⇐” directions fail for semi-abelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all ...

Empty triangles in good drawings of the complete graph

A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges intersects at most once. In any good drawing, the edges of three pairwise connected vertices form a Jordan curve which we call a triangle. We say that a triangle is empty if ...

Periodic de Bruijn triangles: exact and asymptotic results