Related papers: A 2-categorical analysis of context comprehension
In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard…
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.
We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…
It is possible to translate a modified version of K. Worytkiewicz's combinatorial semantics of CCS (Milner's Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled…
The aim of this paper is to study categorified algebraic structures and their pseudo- and lax homomorphisms using the framework of Lawvere $2$-theories, and more generally, (enhanced) $2$-dimensional sketches. The key notion we focus on is…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
An open problem with categorical compositional distributional semantics is the representation of words that are considered semantically vacuous from a distributional perspective, such as determiners, prepositions, relative pronouns or…
This is the second paper in a series on representations over diagrams of abelian categories. We show that, under certain conditions, a compatible family of abelian model categories indexed by a skeletal small category can be amalgamated…
This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…
What makes two computational systems equivalent? Topos theory answers with classifying toposes: a system's semantic content is encoded in the geometric theory it classifies, and two presentations are equivalent when their classifying…
``Classical'' word embeddings, such as Word2Vec, have been shown to capture the semantics of words based on their distributional properties. However, their ability to represent the different meanings that a word may have is limited. Such…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
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…
Recent models of intensional type theory have been constructed in algebraic weak factorization systems (AWFSs). AWFSs give rise to comprehension categories that feature non-trivial morphisms between types; these morphisms are not used in…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
I categorify the definition of fibre bundle, replacing smooth manifolds with differentiable categories, Lie groups with coherent Lie 2-groups, and bundles with a suitable notion of 2-bundle. To link this with previous work, I show that…
Distributed word representations have been demonstrated to be effective in capturing semantic and syntactic regularities. Unsupervised representation learning from large unlabeled corpora can learn similar representations for those words…
Although the categorical arithmetic is not effectively axiomatizable, the belief that the incompleteness Theorems can be apply to it is fairly common. Furthermore, the so-called "essential" (or "inherent") semantic incompleteness of the…
Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categories, and inclusion categories. The objects of a local…
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we show how the context of a `noetherian form', recently…