Frobenius monads and pseudomonoids
نویسندگان
چکیده
منابع مشابه
Ordinals in Frobenius Monads
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 ...
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Frobenius pseudomonoids are higher-dimensional algebraic structures, first studied by Street [34], which categorify the classical algebraic notion of Frobenius algebra [24]. These higher algebraic structures have an important application to logic, since Frobenius pseudomonoids in the bicategory of categories, profunctors and natural transformations, for which the multiplication and unit have ri...
متن کاملCoherence for braided and symmetric pseudomonoids
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in the theory of monoids and commutative monoids, and are generalisations of standard coherence theorems for braided and symmetric monoidal categories.
متن کاملCorecursive 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...
متن کاملAzumaya Monads and Comonads
The definition of Azumaya algebras over commutative rings R requires the tensor product of modules over R and the twist map for the tensor product of any two R-modules. Similar constructions are available in braided monoidal categories, and Azumaya algebras were defined in these settings. Here, we introduce Azumaya monads on any category A by considering a monad (F,m, e) on A endowed with a dis...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2004
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1788852