Related papers: Kernels, lax algebras, d\'ecalage, and supercohere…
Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have…
In this paper we give criteria on integral kernels ensuring that integral operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding trace formulae. In the special…
Let S be a smooth affine algebraic curve, and let S' be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of the mapping class group Mod(S') by showing that its congruence…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
We formulate a conjectural relation between the category of line defects in topologically twisted 3d ${\cal N} = 4$ supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
We introduce completely bounded kernels taking values in L(A,B) where A and B are C*-algebras. We show that if B is injective such kernels have a Kolmogorov decomposition precisely when they can be scaled to be completely contractive, and…
We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `kernel' in which the points of differentiability of each…
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…
We introduce a bialgebra axiom for a pair $(c,\ell)$ of a colax-monoidal and a lax-monoidal structures on a functor $F\colon \mathscr{M}_1\to \mathscr{M}_2$ between two (strict) symmetric monoidal categories. This axiom can be regarded as a…
We give a definition of weak morphism of $T$-algebras, for a $2$-monad $T$, with respect to an arbitrary family $\Omega$ of $2$-cells of the base $2$-category. By considering particular choices of $\Omega$, we recover the concepts of lax,…
In Categorial Topology, given a category (as a "geometric object") we can consider its properties preserved under continuous action (a "deformation") of a comma-propagation operation. However, the Metacategory space, valid for all…
Using the language of double categories we generalise a classical result on finite-product-preserving left Kan extensions, by Ad\'amek and Rosick\'y, to one on left Kan extensions that preserve algebraic structures defined by `suitable'…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
In this short note, we study dg categories with homotopy kernels, whose homotopy categories are known to admit a natural left triangulated structure. Prototypical examples of such dg categories arise as dg quotients of exact dg categories.…
We determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is isomorphic to the 2-category of algebras for this 2-monad.…
The notion of 2--monoidal category used here was introduced by B.~Vallette in 2007 for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the category of quadratic algebras (that is,…
Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…