0000000000631482
AUTHOR
Enrico Vitale
showing 11 related works from this author
Fibred-categorical obstruction theory
2022
Abstract We set up a fibred categorical theory of obstruction and classification of morphisms that specialises to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided to crossed extensions and crossed bimodule butterflies, with in particular a classification of non-abelian extensions of unital associative algebras in terms of Hochschild cohomology.
The snail lemma for internal groupoids
2019
Abstract We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizers.
External derivations of internal groupoids
2008
If His a G-crossed module, the set of derivations of Gin H is a monoid under the Whitehead product of derivations. We interpret the Whitehead product using the correspondence between crossed modules and internal groupoids in the category of groups. Working in the general context of internal groupoids in a finitely complete category, we relate derivations to holomorphisms, translations, affine transformations, and to the embedding category of a groupoid. (C) 2007 Elsevier B.V. All rights reserved.
Bipullbacks of fractions and the snail lemma
2017
Abstract We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a π 0 - π 1 exact sequence associated with a fractor between groupoids internal to a pointed exact category.
On Fibrations Between Internal Groupoids and Their Normalizations
2018
We characterize fibrations and $$*$$ -fibrations in the 2-category of internal groupoids in terms of the comparison functor from certain pullbacks to the corresponding strong homotopy pullbacks. As an application, we deduce the internal version of the Brown exact sequence for $$*$$ -fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and $$*$$ -fibrations in the category of arrows and study when the normalization functor preserves and reflects them. This analysis allows us to give a characterization of protomodular categories using strong homotopy kernels and a generalization of the Snake Lemma.
Drug Prescription and Delirium in Older Inpatients: Results From the Nationwide Multicenter Italian Delirium Day 2015-2016
2019
Objective This study aimed to evaluate the association between polypharmacy and delirium, the association of specific drug categories with delirium, and the differences in drug-delirium association between medical and surgical units and according to dementia diagnosis. Methods Data were collected during 2 waves of Delirium Day, a multicenter delirium prevalence study including patients (aged 65 years or older) admitted to acute and long-term care wards in Italy (2015-2016); in this study, only patients enrolled in acute hospital wards were selected (n = 4,133). Delirium was assessed according to score on the 4 "A's" Test. Prescriptions were classified by main drug categories; polypharmacy w…
"Delirium Day": a nationwide point prevalence study of delirium in older hospitalized patients using an easy standardized diagnostic tool
2016
Background To date, delirium prevalence in adult acute hospital populations has been estimated generally from pooled findings of single-center studies and/or among specific patient populations. Furthermore, the number of participants in these studies has not exceeded a few hundred. To overcome these limitations, we have determined, in a multicenter study, the prevalence of delirium over a single day among a large population of patients admitted to acute and rehabilitation hospital wards in Italy. Methods This is a point prevalence study (called “Delirium Day”) including 1867 older patients (aged 65 years or more) across 108 acute and 12 rehabilitation wards in Italian hospitals. Delirium wa…
Profunctors in Mal’tsev categories and fractions of functors
2013
We study internal profunctors and their normalization under various conditions on the base category. In the Mal'tsev case we give an easy characterization of profunctors. Moreover, when the base category is regular with any regular epimorphism effective for descent, we characterize those profunctors which are fractions of internal functors with respect to weak equivalences. (C) 2012 Elsevier B.V. All rights reserved.
Split extensions, semidirect product and holomorph of categorical groups
2006
Working in the context of categorical groups, we show that the semidirect product provides a biequivalence between actions and points. From this biequivalence, we deduce a two-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the holomorph and inner autoequivalences.
Fibered aspects of Yoneda's regular span
2018
In this paper we start by pointing out that Yoneda's notion of a regular span $S \colon \mathcal{X} \to \mathcal{A} \times \mathcal{B}$ can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category $\mathsf{Fib}(\mathcal{A})$. We study the relationship between these notions and those of internal opfibration and two-sided fibration. This fibrational point of view makes it possible to interpret Yoneda's Classification Theorem given in his 1960 paper as the result of a canonical factorization, and to extend it to a non-symmetric situation, where the fibration given by the product projection $Pr_0 \colon \mathcal{A} \times \mathcal{B} \to \mathcal{A}$ i…
Butterflies in a Semi-Abelian Context
2011
It is known that monoidal functors between internal groupoids in the category Grp of groups constitute the bicategory of fractions of the 2-category Grpd(Grp) of internal groupoids, internal functors and internal natural transformations in Grp, with respect to weak equivalences (that is, internal functors which are internally fully faithful and essentially surjective on objects). Monoidal functors can be equivalently described by a kind of weak morphisms introduced by B. Noohi under the name of butterflies. In order to internalize monoidal functors in a wide context, we introduce the notion of internal butterflies between internal crossed modules in a semi-abelian category C, and we show th…