منابع مشابه
Corecursive Algebras, Corecursive Monads and Bloom Monads
An algebra is called corecursive if from every coalgebra a unique coalgebra-toalgebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization o...
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This paper provides geometrical descriptions of the Frobenius monad freely generated by a single object. These descriptions are related to results connecting Frobenius algebras and topological quantum field theories. In these descriptions, which are based on coherence results for self-adjunctions (adjunctions where an endofunctor is adjoint to itself), ordinals in ε0 play a prominent role. The ...
متن کاملCertification Monads
This entry provides several monads intended for the development of stand-alone certifiers via code generation from Isabelle/HOL. More specifically, there are three flavors of error monads (the sum type, for the case where all monadic functions are total; an instance of the former, the so called check monad, yielding either success without any further information or an error message; as well as ...
متن کاملMonads in double categories
Introduction The development of the formal theory of monads, begun in [23] and continued in [15], shows that much of the theory of monads [1] can be generalized from the setting of the 2-category Cat of small categories, functors and natural transformations to that of a general 2-category. The generalization, which involves defining the 2-category Mnd(K) of monads, monad maps and monad 2-cells ...
متن کاملElgot Monads
It was the idea of Calvin Elgot [4] to use Lawvere theories for the study of the semantics of recursion. He introduced iterative theories as those Lawvere theories in which every ideal morphism e : n → n+p (representing a system of recursive equations in n variables and p parameters) has a unique solution, i. e., a unique morphism e† such that the equation e† = [e†, idp] ·e holds. Elgot proved ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2010
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.12.013