Related papers: Categorical matrix factorizations and monomorphism…
One introduces a class of projective parameterizations that resemble generalized de Jonqui\`eres maps. Any such parametrization defines a birational map $\mathfrak{F}$ of $\pp^n$ onto a hypersurface $V(F)\subset \pp^{n+1}$ with a strong…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
In this survey paper we study parametric versions of writing a matrix in $SL_n (\mathbb{C})$ as a product of lower and upper unitriangular matrices in interchanging order as well as generalizations to other classical groups. We give an…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
We give a general method to build categories of combinatorial manifolds, i.e. categories of combinatorial objects satisfying some local property at every "point", as coreflective subcategories of categories of relational presheaves. To do…
We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As…
We first prove semi-orthogonal decompositions of derived factorization categories arising from sums of potentials of gauged Landau-Ginzburg models, where the sums are not necessarily Thom--Sebastiani type. We then apply the result to the…
By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities fibered over a projective line. In…
We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by…
We construct relative $3$-Calabi--Yau categories related with higher Teichm\"uller theory. We further study their corresponding cosingularity categories and the additive categorification of the corresponding cluster algebras. The input for…
Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $CMS(A)$ be its stable category of maximal CM $A$-modules. Suppose $CMS(A) \cong CMS(B)$ as triangulated categories. Then we show (1) If $A$ is a complete intersection of codimension…
The notion of semi-unital semi-monoidal category was defined a couple of years ago using the so called "Takahashi tensor product" and so far, the only example of it in the literature is complex. In this paper, we use the recently defined…
We show that the bigroupoid of separable symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of finitely semi-simple Calabi-Yau categories are equivalent. To this end, we construct a trace on the category of…
We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. As a consequence we prove a conjecture of Bernevig and Haldane stated in the context of the fractional…
In this paper, we will show that for a smooth quasi-projective variety over $\C,$ and a regular function $W:X\to \C,$ the periodic cyclic homology of the DG category of matrix factorizations $MF(X,W)$ is identified (unde Riemann-Hilbert…
In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the set of isomorphism classes of maximal Cohen--Macaulay modules…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
Over a Cohen-Macaulay ring we consider two extensions of the maximal Cohen-Macaulay modules from the viewpoint of definable subcategories, which are closed under direct limits, direct products and pure submodules. After describing these…
For a finite free EI category, we construct an explicit module over its category algebra. If in addition the category is projective over the ground field, the constructed module is Gorenstein-projective and is a maximal Cohen-Macaulay…