Monads on tensor categories
نویسندگان
چکیده
منابع مشابه
Monads on Dagger Categories
The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when all structure respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and its algebras should satisfy the so-called Frobenius law. Then any monad resolves as an adjunction, with extremal solutions given by the categories of Kleis...
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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 ...
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Introduction. This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a Y/--monad ("strong monad") on a symmetric monoidal closed category ~ carries two canonical structures as closed functor. I f these agree (in which case we call the monad commutative), t...
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Let A be a ring and MA the category of right A-modules. It is well known in module theory that any A-bimodule B is an A-ring if and only if the functor − ⊗A B : MA → MA is a monad (or triple). Similarly, an A-bimodule C is an A-coring provided the functor − ⊗A C : MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of −⊗A B and comodules (or coalgebras) of − ⊗A C...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2002
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00096-2