Related papers: Perfect tangles
Given a complete Heyting algebra we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence we deduce that any complete Boolean algebra is the…
We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…
We study the combinatorics of fully commutative elements in Coxeter groups of type $H_n$ for any $n > 2$. Using the results, we construct certain canonical bases (i.e., IC bases) for non-simply-laced generalized Temperley--Lieb algebras and…
This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…
We survey some features of equivariant instanton partition functions of topological gauge theories on four and six dimensional toric Kahler varieties, and their geometric and algebraic counterparts in the enumerative problem of counting…
In the paper we describe the almost split sequences in the homotopy category of perfect complexes over a gentle algebra.
In this paper, we study $G$-equivariant tensor categories for a finite group $G$. These categories were introduced by Turaev under the name of $G$-crossed categories; the motivating example of such a category is the category of twisted…
We introduce a topology on the ideal space of inductive limits of C*-algebras built by a topological inverse limit of the Fell topologies on the C*-algebras of the given inductive sequence and we produce conditions for when this topology…
The cohomology ring of the moduli space of stable holomorphic vector bundles of rank n and degree d over a Riemann surface of genus g>1 has a standard set of generators when n and d are coprime. When n=2 the relations between these…
We describe dual notions of tangent bundle for an infinity-topos, each underlying a tangent infinity-category in the sense of Bauer, Burke and the author. One of those notions is Lurie's tangent bundle functor for presentable…
We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary…
We introduce perfect cones over topological spaces and study their connection with absolute $B_1$-retracts
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…
Let A be a commutative ring, and \a a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM…
We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…
We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application, we construct an integral version of the…
Using M-theory in physics, Cho, Gang, and Kim (JHEP 2020, 115 (2020) ) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geometric topology and quantum topology. They suggest that…
In previous work the authors introduced a new class of modular quasi-Hopf algebras $D^{\omega}(G, A)$ associated to a finite group $G$, a central subgroup $A$, and a $3$-cocycle $\omega\in Z^3(G, C^x)$. In the present paper we propose a…
In this paper we study representations of conformal nets associated with positive definite even lattices and their orbifolds with respect to isometries of the lattices. Using previous general results on orbifolds, we give a list of all…
We discuss gluing of objects and gluing of morphisms in tensor triangulated categories. We illustrate the results by producing, among other things, a Mayer-Vietoris exact sequence involving Picard groups.