Related papers: Coherence for Modalities
We derive a purely algebraic framework for the identification of hierarchy equations of motion that induce completely positive dynamics and demonstrate the applicability of our approach with several examples. We find bounds on the violation…
The usual coherence theorem of MacLane for categories with multiplication assumes that a certain pentagonal diagram commutes in order to conclude that associativity isomorphisms are well defined in a certain practical sense. The practical…
I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and…
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…
Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…
We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of $\overline{\mathcal{EO}}(n)$ and further prove that $\overline{\mathcal{EO}}(n)\equiv0\pmod4$ for…
We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
In this work, we revisit Auslander-Buchweitz Approximation Theory and find some relations with cotorsion pairs and model category structures. From the notions of relatives generators and cogenerators in Approximation Theory, we introduce…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
Let $k$ be a field of positive characteristic $p$, $R$ be a Gorenstein graded $k$-algebra, and $S=R/J$ be an artinian quotient of $R$ by a homogeneous ideal. We ask how the socle degrees of $S$ are related to the socle degrees of…
We present news proofs of the additivity, resolution and cofinality theorems for the algebraic $K$-theory of exact categories. These proofs are entirely algebraic, based on Grayson's presentation of higher algebraic $K$-groups via binary…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
Coherence theorems are fundamental to how we think about monoidal categories and their generalizations. In this paper we revisit Mac Lane's original proof of coherence for monoidal categories using the Grothendieck construction. This…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor…
We study complexes of stable $\infty$-categories, referred to as categorical complexes. As we demonstrate, examples of such complexes arise in a variety of subjects including representation theory, algebraic geometry, symplectic geometry,…
We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.