Related papers: Internal languages of locally cartesian closed $(\…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…
We show that the category of categories with pullbacks and pullback preserving functors is cartesian closed.
We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…
The basic properties of locally finite triangulated categories are discussed. The focus is on Auslander--Reiten theory and the lattice of thick subcategories.
We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…
Are pairs of words that tend to occur together also likely to stand in a linguistic dependency? This empirical question is motivated by a long history of literature in cognitive science, psycholinguistics, and NLP. In this work we…
While a language assigns a value of either `yes' or `no' to each word, a lattice language assigns an element of a given lattice to each word. An advantage of lattice languages is that joins and meets of languages can be defined as…
We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…
We define an inner product (suitably interpreted) on the K(n)-local spectrum LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner product on E^*BG_+ for suitable K(n)-local ring spectra E. We relate this to the…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
We introduce an extension of the n-ary description logic DLR to deal with attribute-labelled tuples (generalising the positional notation), with arbitrary projections of relations (inclusion dependencies), generic functional dependencies…
In this paper, I establish the categorical structure necessary to interpret dependent inductive and coinductive types. It is well-known that dependent type theories \`a la Martin-L\"of can be interpreted using fibrations. Modern theorem…
We define a quantitative constraint language subsuming two calculi well-known in QSR (Qualitative Spatial Reasoning): Frank's cone-shaped and projection-based calculi of cardinal direction relations. We show how to solve a CSP (Constraint…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Let $G$ be a finite group and $k$ be a field of characteristic $p > 0$. In prior work, we studied endotrivial complexes, the invertible objects of the bounded homotopy category $K^b({}_{kG}\mathbf{triv})$ of $p$-permutation $kG$-modules.…
Connections between homotopy theory and type theory have recently attracted a lot of attention, with Voevodsky's univalent foundations and the interpretation of Martin-Lof's identity types in Quillen model categories as some of the…
We introduce the notion of a $(\Pi,\lambda)$-structure on a C-system and show that C-systems with $(\Pi,\lambda)$-structures are constructively equivalent to contextual categories with products of families of types. We then show how to…
Let $\mathcal{R}$ be an $\mathrm{NIP}$ expansion of $(\mathbb{R},<,+)$ by closed subsets of $\mathbb{R}^n$ and continuous functions $f : \mathbb{R}^m \to \mathbb{R}^n$. Then $\mathcal{R}$ is generically locally o-minimal. It follows that if…
An elementary notion of homotopy can be introduced between arrows in a cartesian closed category $E$. The input is a finite-product-preserving endofunctor $\Pi_0$ with a natural transformation $p$ from the identity which is surjective on…
We establish connections between the concepts of Noetherian, regular coherent, and regular n-coherent categories for Z-linear categories with finitely many objects and the corresponding notions for unital rings. These connections enable us…