منابع مشابه
Descent for Monads
Motivated by a desire to gain a better understanding of the “dimensionby-dimension” decompositions of certain prominent monads in higher category theory, we investigate descent theory for endofunctors and monads. After setting up a basic framework of indexed monoidal categories, we describe a suitable subcategory of Cat over which we can view the assignment C 7→ Mnd(C) as an indexed category; o...
متن کاملMonads of Effective Descent Type and Comonadicity
We show, for an arbitrary adjunction F U : B → A with B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type, meaning that the free T-algebra functor F : A → AT is comonadic. This result is applied to several situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed ...
متن کاملProfinite Monads, Profinite Equations, and Reiterman's Theorem
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e. classes of finite algebras closed under finite products, subalgebras and quotients. In this paper Reiterman’s theorem is generalised to finite Eilenberg-Moore algebras for a monad T on a variety D of (ordered) algebras: ...
متن کاملLax theorem and finite volume schemes
This work addresses a theory of convergence for finite volume methods applied to linear equations. A non-consistent model problem posed in an abstract Banach space is proved to be convergent. Then various examples show that the functional framework is non-empty. Convergence with a rate h 1 2 of all TVD schemes for linear advection in 1D is an application of the general result. Using duality tec...
متن کاملEffective Descent Morphisms in Categories of Lax Algebras
In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...
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ژورنال
عنوان ژورنال: Tbilisi Mathematical Journal
سال: 2015
ISSN: 1875-158X
DOI: 10.1515/tmj-2015-0001