Related papers: Additive Enrichment from Coderelictions
We extend to general Cartesian categories the idea of Coherent Differentiation recently introduced by Ehrhard in the setting of categorical models of Linear Logic. The first ingredient is a summability structure which induces a partial…
The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids (or semigroups) in cryptography. To overcome this issue we propose to look at monoids with only big representations, in…
Cofunctors are a kind of map between categories which lift morphisms along an object assignment. In this paper, we introduce cofunctors between categories enriched in a distributive monoidal category. We define a double category of enriched…
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly's and Mac Lane's…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
Joyal and Street note in their paper on braided monoidal categories [Braided tensor categories, Advances in Math. 102(1993) 20-78] that the 2-category V-Cat of categories enriched over a braided monoidal category V is not itself braided in…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
The monoidal properties of the Dold-Kan correspondence have been studied in homotopy theory, notably by Schwede and Shipley. Changing the enrichment of an enriched, tensored, and cotensored category along the Dold-Kan correspondence does…
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…
We present an unbiased theory of symmetric multicategories, where sequences are replaced by families. To be effective, this approach requires an explicit consideration of indexing and reindexing of objects and arrows, handled by the double…
We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for…
Linearly distributive categories (LDC), introduced by Cockett and Seely to model multiplicative linear logic, are categories equipped with two monoidal structures that interact via linear distributivities. A seminal result in monoidal…
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…
Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity…
Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this…
The theory of derivators provides a convenient abstract setting for computing with homotopy limits and colimits. In enriched homotopy theory, the analogues of homotopy (co)limits are weighted homotopy (co)limits. In this thesis, we develop…
We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical…
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics.…