Coidempotent subcoalgebras and short exact sequences of finitary 2-representations

In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations

Surveillance in Hogwarts: Dumbledore's balancing act between managerialism and anarchism

This article considers the fictional depiction of surveillance in Harry Potter, and compares the two different models of school leadership represented by Dolores Umbridge and Albus Dumbledore. The Harry Potter books put forward a vision of school leadership that affirms the necessity of surveillance. The optimal degree of surveillance means a fine balance between managerialism and anarchism. Neither a panoptic gaze of discipline and management which aims to control the minutest details of a person’s action, nor the absence of surveillance is desirable. Hogwarts is a surveillance school, and the difference between the two principals, both of whom insist on the maintenance of a hierarchical power structure, lies in the extent to which surveillance is in operation. Whereas Umbridge represents the failure of extreme managerialism which only results in fierce resistance, Dumbledore is portrayed as the desirable model of a temperate leader who, through reducing management and developing trust, succeeds in cultivating in students a version of discipline that is not based on external behaviour but on internal values

Irreducible representations of the symmetric groups from slash homologies of p-complexes

In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by using the unsigned boundary map and taking coefficients of chains modulo $p$. We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case, this is also a $p$-complex of representations of the symmetric group of rank $n$ - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a $p$-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called $p$-standard tableaux.Comment: 16 pages, 2 figures. Rewritten the proof of first theorem. Substantial rearrangement of materials in other sections. Comments welcome