Related papers: Presenting Distributive Laws
The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of "truth values"), via an appropriate distributive law…
Natural logic offers a powerful relational conception of meaning that is a natural counterpart to distributed semantic representations, which have proven valuable in a wide range of sophisticated language tasks. However, it remains an open…
For a (co)monad T_l on a category M, an object X in M, and a functor \Pi: M \to C, there is a (co)simplex Z^*:=\Pi T_l^{* +1} X in C. Our aim is to find criteria for para-(co)cyclicity of Z^*. Construction is built on a distributive law of…
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and…
Distributive laws are important for algebraic reasoning in arithmetic and logic. They are equally important for algebraic reasoning about concurrent programs. In existing theories such as Concurrent Kleene Algebra, only partial correctness…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
Using methods of computer algebra, especially Gr\"obner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous)…
The recent notion of graded modal types provides a framework for extending type theories with fine-grained data-flow reasoning. The Granule language explores this idea in the context of linear types. In this practical setting, we observe…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical…
Many studies were recently done for investigating the properties of contextual language models but surprisingly, only a few of them consider the properties of these models in terms of semantic similarity. In this article, we first focus on…
It is known that the construction of the frame of ideals from a distributive lattice induces a monad whose algebras are precisely the frames and frame homomorphisms. Using the Fakir construction of an idempotent approximation of a monad, we…
If T is a commutative monad on a cartesian closed category, then there exists a natural T-bilinear pairing from T(X) times the space of T(1)-valued functions on X ("integration"), as well as a natural T-bilinear action on T(X) by the space…
Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'd distributive law between the comonad given…
The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…