The formal theory of monoidal monads
نویسندگان
چکیده
منابع مشابه
Lax Formal Theory of Monads, Monoidal Approach to Bicategorical Structures and Generalized Operads
Generalized operads, also called generalized multicategories and T -monoids, are defined as monads within a Kleisli bicategory. With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors in different contexts, with examples including symmetric multicategories, topological spaces, globular operads and Lawvere theories. In this paper we study f...
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In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, taken together, we have: there is a 1-1 correspondence between commutative monads and symmetric monoidal monads (Theorem 2.3 below). The main computational work needed consists in constructing an equivalenc...
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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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In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterise its n-arrows using a graphical calculus that we develop here. The hom-spaces are appropriately fibrant, indeed are nerves of categories, which indicates that all of the expected coherence equations in each dimension are present. To justify our terminology, we prove tha...
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 ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2012.02.030