Related papers: Correspondence functors and lattices
Polynomial functors are sums of covariant representable functors from the category of sets to itself. They have a robust theory with many applications -- from operads and opetopes to combinatorial species. In this paper, we define a…
In prior work we described how the Cuntz-Pimsner construction may be viewed as a functor. The domain of this functor is a category whose objects are $C^*$-correspondences and morphisms are isomorphism classes of certain pairs comprised of a…
In this paper we consider a general way of constructing profinite struc- tures based on a given framework - a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family…
Let A be a finitely-generated commutative ring and k a noetherian commutative ring. We show that, in the category of functors from finitely-generated projective A-modules to k-modules, each finitely-generated polynomial functor is…
Kei Yuen Chan and Kayue Daniel Wong constructed a functor from the category of Harish-Chandra modules of $\mathrm{GL}(n, \mathbb C)$ to the category of modules over graded Hecke algebra $\mathbb H_m$ of type A. This functor has several nice…
We construct A-infinity functors between Fukaya categories associated to monotone Lagrangian correspondences between compact symplectic manifolds. We then show that the composition of A-infinity functors for correspondences is homotopic to…
We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category…
Kirillov has described a McKay correspondence for finite subgroups of PSL_{2}(C) that associates to each `height' function an affine Dynkin quiver together with a derived equivalence between equivariant sheaves on the projective line P^1…
We prove that every finite distributive lattice $D$ can be represented as the congruence lattice of a rectangular lattice $K$ in which all congruences are principal. We verify this result in a stronger form as an extension theorem.
Auslander and Kleiner proved in 1994 an abstract version of Green correspondence for pairs of adjoint functors between three categories. They produce additive quotients of certain subcategories giving the classical Green correspondence in…
We study projective functors (i.e. direct summands of compositions of translations through walls) for parabolic versions of $\cO$ as well as for integral regular blocks outside the critical hyperplanes in the symmetrizable Kac-Moody case.…
To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we…
Given associative unital algebras $A$ and $B$ and a complex $T^\bullet$ of $B-A-$bi\-modules, we give necessary and sufficient conditions for the total derived functors, $\Rh_A(T^\bullet,?):\D(A)\longrightarrow\D(B)$ and…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. A general formula…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…
We interpret the construction of relative Cuntz-Pimsner algebras of correspondences in terms of the correspondence bicategory, as a reflector into a certain sub-bicategory. This generalises a previous characterisation of absolute…
We define certain class of correspondences of polarized representations of $C^*$-algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…