Related papers: Coherence for logicians

This paper elaborates on a new approach of the question of the proof-theoretic study of concurrent interaction called "proofs as schedules". Observing that proof theory is well suited to the description of confluent systems while…

Abstract. Matching logic cannot handle concurrency. We introduce concurrent matching logic (CML) to reason about fault-free partial correctness of shared-memory concurrent programs. We also present a soundness proof for concurrent matching…

We give a natural-deduction-style type theory for symmetric monoidal categories whose judgmental structure directly represents morphisms with tensor products in their codomain as well as their domain. The syntax is inspired by Sweedler…

Univalent categories constitute a well-behaved and useful notion of category in univalent foundations. The notion of univalence has subsequently been generalized to bicategories and other structures in (higher) category theory. Here, we…

This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…

We prove that the homotopy theory of parsummable categories (as defined by Schwede) with respect to the underlying equivalences of categories is equivalent to the usual homotopy theory of symmetric monoidal categories. In particular, this…

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…

We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution…

We prove that a pair of singularities related by a transformation arising from the McKay correspondence are orbifold equivalent. From this we deduce a new proof of a McKay type equivalence for the matrix factorization categories.

Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…

We establish a large class of homotopy coherent Morita-equivalences of Dold-Kan type relating diagrams with values in any weakly idempotent complete additive $\infty$-category; the guiding example is an $\infty$-categorical Dold-Kan…

We derive two geometric approaches to categorification of quantum invariants of links associated to an arbitrary compact simple Lie group $^L{G}$. In part I, we describe the first approach, based on an equivariant derived category of…

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

Quantum indistinguishability by path identity generates a new way of optical coherence, called ``induced coherence". The phenomenon, originally uncovered by Zou, Wang, and Mandel's experiment, is an emerging notion in modern quantum…

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…

We prove that a certain $\omega$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\omega$-equivalence. Further, appropriate truncations of it give models for the…

This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves.…

Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and conjunction; the internal hom interprets linear implication.…

Quantum coherence is one of the primary non-classical features of quantum systems. While protocols such as the Leggett-Garg inequality (LGI) and quantum tomography can be used to test for the existence of quantum coherence and dynamics in a…