heck?! How do you even explain what a monad is? John Baez, In category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle...

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

and side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a functor with additional...

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

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...

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

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...

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

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...

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...

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...

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

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

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...

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

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

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...

lemma in the theory of model categories. Kleisli category Given a monad T, the Kleisli category of T is the full subcategory of the category of T-algebras...

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

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...

can be given the structure of a monad; this monad is called the environment (or reader) monad. If A is an abelian category and A is an object of A, then...

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...

measurable spaces; Markov categories such as the category of Markov kernels; Probability monads such as Giry monad. W. Lawvere, The category of probabilistic mappings...

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

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...

gives a monad on the category of sets, while any "finitary" monad on the category of sets arises from a Lawvere theory. However, a monad describes algebraic...

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...

monads (and hence adjoint functors) since monads can be viewed as monoid objects in endofunctor categories. Simplicial category PROP (category theory)...

for short, is an intermediate structure between functors and monads. In Category Theory they are called Closed Monoidal Functors. Applicative functors...

\gamma ,\eta )} in the monoidal category of endofunctors on R - M o d {\displaystyle R{\text{-}}{\mathsf {Mod}}} (it is a monad) satisfying some finiteness...