Recent investigations of lax algebras—in generalization of Barr’s relational algebras—make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on t...

If S is an order-adjoint monad, that is, a monad on Set that factors through the category of ordered sets with left adjoint maps, then any monad morphism τ : S → T makes T orderadjoint, and the Eilenberg-Moore category of T is monadic over the category of monoids in the Kleisli category of S.

Galois comodules over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of Galois functors over some comonad (or monad) on any category and in the first section of the present paper we investigate the role of the relative injectives (projectives) in this context. Then we generalise the notion of corings (derived from an entwining of a...

In this work we generalize previous constructions of fuzzy set categories, introduced in [5], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational. In the final part of the paper, the L-fu...

Inspired by recent work of Batanin and Berger on the homotopy theory of operads, a general monad-theoretic context for speaking about structures within structures is presented, and the problem of constructing the universal ambient structure containing the prescribed internal structure is studied. Following the work of Lack, these universal objects must be constructed from simplicial objects ari...

The Functional Analysis Screening Tool (FAST) is a 16-item questionnaire about antecedent and consequent events that might be correlated with the occurrence of problem behavior. Items are organized into 4 functional categories based on contingencies that maintain problem behavior. We assessed interrater reliability of the FAST with 196 problem behaviors through independent administration to pai...

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...

It is shown that five apparently irreconcilable claims about the clausal syntax of Irish can be reconciled in a natural, base-generated LFG analysis that builds on the standard LFG theory of endocentricity and coheads/extended heads, the LFG projection architecture, and Toivonen’s (2001) work on nonprojecting categories and c-structure adjunction. The analysis also builds on McCloskey’s (1996) ...

Given an arbitrary locally finitely presentable category K and finitary monads T and S on K , we characterize monad morphisms α : S −→ T with the property that the induced functor α∗ : K T −→ K S between the categories of Eilenberg-Moore algebras is fully faithful. We call such monad morphisms dense and give a characterization of them in the spirit of Beth’s definability theorem: α is a dense m...

A wealth of animal data implicates the amygdala in aspects of emotional processing. In recent years, functional neuroimaging and neuropsychological studies have begun to refine our understanding of the functions of the amygdala in humans. This literature offers insights into the types of stimuli that engage the amygdala and the functional consequences that result from this engagement. Specific ...