Extensions of symmetric cat-groups

On Extensions of Simple Modules over Symmetric and Algebraic Groups

Homomorphisms and Higher Extensions for Schur Algebras and Symmetric Groups

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined.

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Left Kan Extensions Over !-Cat

An existing procedure to compute left Kan extensions over the ground category Set also computes left Kan extensions over the ground categories Cat, 2-Cat, n-Cat for any n and indeed !-Cat. Therefore extension data struc-tured in this manner already can make use of the left Kan extension notion of a best possible approximation. Examples include systems of labeled transition systems and certain h...

Extensions of Groups

To better understand groups it is often useful to see how a group can be built from smaller groups. For example, given two groups G and H, we can form the direct product G × H. This new group can be studied in terms of the two pieces from which it is built. However, the direct product construction is too special to understand most groups. In other words, most groups are not expressible as the d...