Related papers: Multisorted modules and their model theory
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
Using the $\infty$-categorical enhancement of mixed Hodge modules constructed by the author in a previous paper, we explain how mixed Hodge modules canonically extend to algebraic stacks, together with all the $6$ operations and weights. We…
Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel papers is to show that for any finite dimensional algebra there…
For any ring $A$ and a small, preadditive, Hom-finite, and locally bounded category $Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors from $Q$ to the category of…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…
In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of…
We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat$^1$-objects that are both obtained by pullback diagrams with extra…
We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence…
In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered…
We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they may be used to describe the components of…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…
We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a…
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…