Sectional category of fibrations of fibre $ K(\mathbb{Q}, 2k)$

The sectional category of spherical fibrations

We give homological conditions which determine sectional category, secat, for rational spherical fibrations. In the odd dimensional case the secat is the least power of the Euler class which is trivial. In the even dimensional case secat is one when a certain homology class in twice the dimension of the sphere is −1 times a square. Otherwise secat is two. We apply our results to construct a fib...

Derived Category of Toric Fibrations

In this paper, we give a structure theorem for the derived category D(X) of a toric fibration X over P with fiber Y provided that Y has a full strongly exceptional collection of line bundles.

Fibrations in ∞-category Theory

In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the constructions these fibrations make available to end-users of higher category theory.

A Combinatorial Proof of a Relationship Between Maximal $(2k-1, 2k+1)$-Cores and $(2k-1, 2k, 2k+1)$-Cores

Integer partitions which are simultaneously t–cores for distinct values of t have attracted significant interest in recent years. When s and t are relatively prime, Olsson and Stanton have determined the size of the maximal (s, t)-core κs,t. When k > 2, a conjecture of Amdeberhan on the maximal (2k − 1, 2k, 2k + 1)-core κ2k−1,2k,2k+1 has also recently been verified by numerous authors. In this ...

Category of Polygroup Objects