category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...

that implement monad (e.g. Option, List, etc.). Both the concept of a monad and the term originally come from category theory, where a monad is defined as...

It is one of the main examples of a probability monad. It is implicitly used in probability theory whenever one considers probability measures which...

Adjoint functors Galois connection Pontryagin duality Affine scheme Monad (category theory) Comonad Combinatorial species Exact functor Derived functor Dominant...

invention Monad (biology), a historical term for a simple unicellular organism Monad (category theory), a construction in category theory Monad (functional...

In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...

especially in category theory, the codensity monad is a fundamental construction associating a monad to a wide class of functors. The codensity monad of a functor...

theory, infinitary Lawvere theory, and finite-product theory. Algebraic theory Clone (algebra) Monad (category theory) Lawvere theory at the nLab Hyland, Martin;...

In category theory, a Kleisli category is a category naturally associated to any monad T. It is equivalent to the category of free T-algebras. The Kleisli...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of...

a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many expositions...

In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat...

algebras of its associated monad, in category theory Monadic, in computer programming, a feature, type, or function related to a monad (functional programming)...

In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute...

The term monad (from Ancient Greek μονάς (monas) 'unity' and μόνος (monos) 'alone') is used in some cosmic philosophy and cosmogony to refer to a most...

Eilenberg-Moore categories of finitary monads. Both these, in turn, are equivalent to categories of algebras of Lawvere theories. Working with monads permits...

presents, in some 90 paragraphs, a metaphysics of simple substances, or monads. During his last stay in Vienna from 1712 to September 1714, Leibniz wrote...

list. This operation Σ mapping category C to Σ(C) can be extended to a strict 2-monad on Cat. If, in a monoidal category, A ⊗ B {\displaystyle A\otimes...

the underlying sets are not in bijection. Stoch is the Kleisli category of the Giry monad. This in particular implies that there is an adjunction H o m...

ultrafilter monad is the codensity monad of the inclusion of the category of finite sets into the category of all sets. Similarly, the ultraproduct monad is the...

In category theory, a strong monad is a monad on a monoidal category with an additional natural transformation, called the strength, which governs how...

1007/BFb0092872. ISBN 978-3-540-11211-2. Jacobs, Bart (2018). "From probability monads to commutative effectuses". Journal of Logical and Algebraic Methods in...

Leinster, Tom (2013), "Codensity and the ultrafilter monad", Theory and Applications of Categories, 28: 332–370, arXiv:1209.3606, Bibcode:2012arXiv1209...

Natural transformation Adjoint functor Monad (category theory) Variety of algebras Cartesian closed category Jacobson (2009), Proposition 1.6, p. 44...

Leinster, Tom (2013). "Codensity and the ultrafilter monad" (PDF). Theory and Applications of Categories. 28: 332–370. arXiv:1209.3606. Bibcode:2012arXiv1209...

other branches of mathematics, including computability theory, category theory, and set theory. Formal semantics is the formal specification of the behaviour...

closed category, and furthermore a dagger compact category. The category Rel can be obtained from the category Set as the Kleisli category for the monad whose...

In category theory, a branch of mathematics, a monoidal monad ( T , η , μ , T A , B , T 0 ) {\displaystyle (T,\eta ,\mu ,T_{A,B},T_{0})} is a monad ( T...

only five laws. In category theory, the Kleisli categories of all monads form a proper subset of Hughes arrows. While Freyd categories were believed to...

known contribution to metaphysics is his theory of monads, as exposited in Monadologie. He proposes his theory that the universe is made of an infinite...