Monoidal bicategories, differential linear logic, and analytic functors
We develop further the theory of monoidal bicategories by introducing and studying bicate-
gorical counterparts of the notions of a linear explonential comonad, as considered in the …
gorical counterparts of the notions of a linear explonential comonad, as considered in the …
[PDF][PDF] Effectful semantics in bicategories: strong, commutative, and concurrent pseudomonads
Moggi [59, 60] famously observed that the structure of effectful computation is captured by
the category-theoretic notion of strong monad. This gives a framework for constructing new …
the category-theoretic notion of strong monad. This gives a framework for constructing new …
Concurrent monads for shared state
E Rivas, T Uustalu - Proceedings of the 26th International Symposium on …, 2024 - dl.acm.org
In the monad-based approach to functional programming with effects, sequential
composition, the primary high-level control structure for combining effectful functions, takes a …
composition, the primary high-level control structure for combining effectful functions, takes a …
Enriched duality in double categories II: modules and comodules
V Aravantinos-Sotiropoulos… - arXiv preprint arXiv …, 2024 - arxiv.org
In this work, we continue the investigation of certain enrichments of dual algebraic structures
in monoidal double categories, that was initiated in [Vas19]. First, we re-visit monads and …
in monoidal double categories, that was initiated in [Vas19]. First, we re-visit monads and …
Transposing cartesian and other structure in double categories
E Patterson - arXiv preprint arXiv:2404.08835, 2024 - arxiv.org
The cartesian structure possessed by morphisms like relations, spans, and profunctors is
elegantly expressed by universal properties in double categories. Though cartesian double …
elegantly expressed by universal properties in double categories. Though cartesian double …
Premonoidal and Kleisli double categories
B Femić - arXiv preprint arXiv:2401.17494, 2024 - arxiv.org
We generalize to double categories the recently introduced notion of premonoidal
bicategories of Paquet and Saville. We investigate the relation of a premonoidal double …
bicategories of Paquet and Saville. We investigate the relation of a premonoidal double …