Related papers: Invertible cells in $\omega$-categories
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…
We prove that any weakly idempotent complete $d$-exact category is equivalent to a $d$-cluster tilting subcategory of a weakly idempotent complete exact category, and that any weakly idempotent complete algebraic $(d+2)$-angulated category…
In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak fibration category can be "completed" into a full model…
The category of double categories and double functors is equipped with a symmetric closed monoidal structure. For any double category $\mathbb A$, the corresponding internal hom functor $|[ \mathbb A,-]|$ sends a double category $\mathbb B$…
In this note, we study the connection between Gray tensor product and suspension. We derive a characterization of weak equivalences as fully faithful and essentially surjective functors. We construct the $co$ duality, a weak involution that…
In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.
We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…
We conjecture that every infinite group $G$ can be partitioned into countably many cells $G=\bigcup_{n\in\omega}A_n$ such that $cov(A_nA_n^{-1})=|G|$ for each $n\in\omega$. Here $cov(A)=\min\{|X|:X\subseteq G, G=XA\}$. We confirm this…
Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
It is well-known that a class of all modules, which are torsion-free with respect to a set of ideals, is closed under injective envelopes. In this paper, we consider a kind of a dual to this statement - are the divisibility classes closed…
In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is $\bf{0^{(\alpha)}}$ for…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…