Related papers: Bicartesian Coherence Revisited

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

We demonstrate the simple and deep equivalence between quantum coherence and nonclassicality and the definite way in which they determine metrological resolution. Moreover, we define a coherence observable consistent with a classical…

Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…

To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…

We define strict and weak duality involutions on 2-categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2-category with a strict duality involution. For this purpose we…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…

We study coherence of graph products and Coxeter groups and obtain many results in this direction.

The purpose of this article is to study the existence of Deligne's tensor product of abelian categories by comparing it with the well-known ten- sor product of finitely cocomplete categories. The main result states that the former exists…

We retrieve the graded commutative algebra structure of rack and quandle cohomology by purely algebraic means.

A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and…

We prove properness of (co)Cartesian fibrations as well as a straightening and unstraightening equivalence, which is compatible with cartesian products, when the base is the nerve of a small category.

A symmetric monoidal category is a category equipped with an associative and commutative (binary) product and an object which is the unit for the product. In fact, those properties only hold up to natural isomorphisms which satisfy some…

We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of univalent…

We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…

We prove that every locally Cartesian closed $\infty$-category with subobject classifier has a strict initial object and disjoint and universal binary coproducts.

We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of…

We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.