Generalised bialgebras and entwined monads and comonads
نویسندگان
چکیده
منابع مشابه
Azumaya 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...
متن کاملMonads and Comonads on Module Categories
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...
متن کاملMonads and Comonads in Module Categories
Let A be a ring and MA the category of A-modules. It is well known in module theory that for any A-bimodule B, 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 ...
متن کاملCoherence for monoidal monads and comonads
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor (this means that it preserves the monoidal structure up to a natural transformation that need not be an isomorphism). These results are proved first in the ...
متن کاملCost-analysis: How do monads and comonads differ?
Monads are a de facto standard for the type-based analysis of impure aspects of programs, such as runtime cost [9, 5]. Recently, the logical dual of a monad, the comonad, has also been used for the cost analysis of programs, in conjunction with a linear type system [6, 8]. The logical duality of monads and comonads extends to cost analysis: In monadic type systems, costs are (side) effects, whe...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2015
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2014.10.013