A functorial approach to monomorphism categories for species I

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalized species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit computations as in the case of Ringel and Schmidmeier.

Torsion Pairs and Ringel Duality for Schur Algebras

Let A be a finite-dimensional algebra over an algebraically closed field. We use a functorial approach involving torsion pairs to construct embeddings of endomorphism algebras of basic projective A–modules P into those of the torsion submodules of P. As an application, we show that blocks of both the classical and quantum Schur algebras S(2,r) and Sq(2,r) in characteristic p > 0 are Morita equivalent as quasi-hereditary algebras to their Ringel duals if they contain 2pk simple modules for some k.

Fusion of interfaces in Landau-Ginzburg models: a functorial approach

We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

The twofold way of super holonomy

There are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops. Either theory comes with its own version of invariance of vectors and subspaces under holonomy. By our first main result, the Twofold Theorem, these definitions are equivalent. Our proof is based on the Comparison Theorem, our second main result, which characterises Galaev’s holonomy algebra as an algebra of coefficients, building on previous results. As an application, we generalise some of Galaev’s results to