H. Kleisli. Every standard construction is induced by a pair of adjoint functors. Proc. Amer. Math. Soc., 16:544--546, 1965.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....identification of monads, in particular as associated with adjoints, can be seen as initiated around 1958. Godement was at that time one of the very first authors to use monads, even if then only named standard constructions . Huber in 1961 showed that adjoint pairs give rise to monads. Kleisli [18] and Eilenberg and Moore [7] proved the converse in 1965. The construct of a Kleisli category was thus made explicit in those contributions. Lawvere [19] introduced universal algebra into category theory. This can be seen as the birth of the term monad. These developments then contain all ....

H. Kleisli, Every standard construction is induced by a pair of adjoint functors, Proc. Amer. Math. Soc. 16 (1965), 544--546.

....the structure of a category, by defining an appropriate composition. The following construction can also be found in [GTWW77] on page 74 (footnote 10) where functions are used instead of tuples. It is also possible to generalize this construction, which is then known as a Kleisli category [Kle65]. In this paper we will not focus on monads or Kleisli categories. 6.1.2 Definition (category of forests) Let # be a ranked alphabet. We define the category T # by ObT # = N 0 , T # (m, n) T #X n ) m where # l, m,n # ObT # : # f = f i ) l i=1 # T # (l, m) # g = g j ) ....

H. Kleisli. Every standard construction is induced by a pair of adjoint functors,. In Proc. Amer. Math. Soc., volume 16, pages 544--546, 1965.

....5 5 We provide a function Memoize (f) in our system to convert any f of type unit 1a into a memoized function. We have an important reason for choosing this tree of unions of singletons representation for sets. Kleisli is based on the notion of monads in the form of Kleisli triples [7]. Thus, its main operator is the homomorphism S ff(x) j x 2 eg, which is the big union of f(o1 ) f(on ) for the elements o1 , on in e. This fact implies that the set union operation is expected to be the most frequently used operator in Kleisli. So it is desirable to make it as cheap ....

H. Kleisli. Every standard construction is induced by a pair of adjoint functors. Proc. Amer. Math. Soc., 16:544--546, 1965.

....way, and if, given that construction, every monad comes from an adjoint functor. In the setting of categories, this is achieved by either the Eilenberg Mooreconstruction, which will turn out to have a slightly different background in this context, or the Kleisli construction as introduced in [8]. The latter is given in its most natural form as a construction on objects introduced as algebraic theories in extension form in [11] and called Kleisli triples in [13] both that description and the Kleisli construction generalize quite naturally to precategories and, in fact, to arbitrary ....

Kleisli, H.: Every standard construction is induced by a pair of adjoint functors. Proc. Amer. Math. Soc. 16 (1065), 544--546.

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H. Kleisli. Every standard construction is induced by a pair of adjoint functors. Proc. Amer. Math. Soc., 16:544--546, 1965.

No context found.

H. Kleisli. Every standard construction is induced by a pair of adjoint functors. In Proceedings of the American Mathematical Society, volume 16, pages 544-546, 1965.

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