The Verdier Hypercovering Theorem

2012 ◽  
Vol 55 (2) ◽  
pp. 319-328 ◽  
Author(s):  
J. F. Jardine
Keyword(s):  
Broad Sense ◽  
Homotopy Category ◽  
Homotopy Classes ◽  
Theoretic Proof ◽  
Simplicial Sheaves ◽  
Simplicial Homotopy

AbstractThis note gives a simple cocycle-theoretic proof of the Verdier hypercovering theorem. This theorem approximates morphisms [X, Y] in the homotopy category of simplicial sheaves or presheaves by simplicial homotopy classes of maps, in the case where Y is locally fibrant. The statement proved in this paper is a generalization of the standard Verdier hypercovering result in that it is pointed (in a very broad sense) and there is no requirement for the source object X to be locally fibrant.

scholarly journals A study of some aspects of topological groups

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 55-65
Author(s):  
M.R. Adhikari ◽  
M. Rahaman
Keyword(s):  
Topological Group ◽  
Group Structure ◽  
Base Point ◽  
Homotopy Category ◽  
Topological Spaces ◽  
Topological Groups ◽  
Homotopy Classes ◽  
Continuous Maps

The aim of this paper is to find a generalization of topological groups. The concept arises out of the investigation to obtain a group structure on the set [X,Y], of homotopy classes of maps from a space X to a given space Y for all X which is natural with respect to X. We also study the generalized topological groups. Finally, associated with each generalized topological group we construct a contra variant functor from the homotopy category of pointed topological spaces and base point preserving continuous maps to the category of groups and homomorphism.

scholarly journals A closed simplicial model category for proper homotopy and shape theories

1998 ◽  
Vol 57 (2) ◽  
pp. 221-242 ◽  
Author(s):  
J.M. García-Calcines ◽  
M. Garcia-Pinillos ◽  
L.J. Hernández-Paricio
Keyword(s):  
Exact Sequence ◽  
The Other ◽  
Model Category ◽  
Homotopy Category ◽  
Finite Covering ◽  
Covering Dimension ◽  
Homotopy Classes ◽  
Exterior Space ◽  
Proper Maps ◽  
Proper Homotopy

In this paper, we introduce the notion of exterior space and give a full embedding of the category P of spaces and proper maps into the category E of exterior spaces. We show that the category E admits the structure of a closed simplicial model category. This technique solves the problem of using homotopy constructions available in the localised category HoE and in the “homotopy category” π0E, which can not be developed in the proper homotopy category.On the other hand, for compact metrisable spaces we have formulated sets of shape morphisms, discrete shape morphisms and strong shape morphisms in terms of sets of exterior homotopy classes and for the case of finite covering dimension in terms of homomorphism sets in the localised category.As applications, we give a new version of the Whitehead Theorem for proper homotopy and an exact sequence that generalises Quigley's exact sequence and contains the shape version of Edwards-Hastings' Comparison Theorem.

Pull-Backs in Homotopy Theory

1976 ◽  
Vol 28 (2) ◽  
pp. 225-263 ◽  
Author(s):  
Michael Mather
Keyword(s):  
Homotopy Theory ◽  
Homotopy Category ◽  
Topological Spaces ◽  
Homotopy Classes ◽  
Different Dimensions

The (based) homotopy category consists of (based) topological spaces and (based) homotopy classes of maps. In these categories, pull-backs and push-outs do not generally exist. For example, no essential map between Eilenberg-MacLane spaces of different dimensions has a kernel. In this paper we define homotopy pull-backs and push-outs, which do exist and which behave like pull-backs and push-outs, and we give some of their properties. Applications may be found in [3; 5; 6 and 14].

Beetles of the family Cryptophagidae (Coleoptera) in the collection of Zoological Museum of Taras Shevchenko National University of Kyiv

2019 ◽  
Vol 17 (2) ◽  
pp. 10-24 ◽  
Author(s):  
K. Ocheretna
Keyword(s):  
Species Identification ◽  
Broad Sense ◽  
Zoological Museum ◽  
World War ◽  
Identification Number ◽  
Comprehensive List ◽  
Carpathian Region ◽  
The Family ◽  
National University ◽  
Collection Sites

The Cryptophagidae collection (Coleoptera: Cucujoidea) deposited at the Zoological Museum of the Taras Shevchenko National University of Kyiv (ZMKU) is described. The main authors of the collection are well-known researchers from the 1910–1930s, Orest Marcu and Karl Penecke. This is the largest collection of cryptophagids among the natural museums of Ukraine containing 304 specimens belonging to 85 species of 13 genera. In addition, 15 specimens of 5 species belonging to the families Erotylidae, Biphyllidae and Languriidae were among Cryptophagidae specimens. The collection, according to information available in the ZMKU, came to the museum not earlier than 1947 as the indemnity for the results of the II World War, most likely from Chernivtsi, where Marcu and Penecke worked. The vast majority of specimens is collected in the territory of modern Romania and Ukraine, and many specimens came from Chernivtsi. A table with an overview of all key details of the specimens is given, in which there are 6 fields: the name of the species on the label, details on the species identification, number of specimens, collection locality with the name of collector and remarks on the specimen, in particular, the instructions for decoding collection sites from the original labels. Annotations are made on the amount of the collection and the most important specimens and re-identification for each of the 13 genera. Some specimens are lost, probably during numerous collection migrations. In particular, some species (Cryptophagus simplex, C. lapidicola, C. nitidulus, Caenoscelis subdeplanata, Atomaria grandicollis, A. peltata, etc.) are represented in the collection only by the labels. The collection is important for the analysis of the composition of the fauna of the Carpathian region in the broad sense, since some species are encountered in the collection rarely; therefore it is important to clarify their locations to form the most comprehensive list of species of the Cryptophagids in the region. Several species of the family were included on the actual list of the fauna of the region on the basis of the study of this collection, in particular: Atomaria linearis, A. analis, A. apicalis, A. gravidula, Cryptophagus fasciatus, C. setulosus, etc.

The Strict and the broad sense of Symmetry in vitruvius’ de Architectura

2018 ◽  
Vol 29 (3) ◽  
pp. 353-363
Author(s):  
Pavlos Lefas ◽  
Keyword(s):  
Broad Sense

KONTEKS IBADAH MENURUT AL-QURAN

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Abdul Kallang
Keyword(s):  
Broad Sense ◽  
Wide Scope

AbstractWorship to God in the broad sense, also has a wide scope. Some are directly or indirectly. Directly is by way of worship hablun minallah. Indirectly is by fostering hablun minannas according to the command of God. The doctrine of worship should not be superficially understood, in which some interpret the worship to be merely a mahdhah worship, or only concerning ritual aspects such as prayer, fasting, and hajj. In fact, worship in the broad sense must also be understood, namely everything that is pleasing and favored by God in the form of deeds and speech is included worship. Keywords: Worship, Al-Quran, hablun minallah, hablun minannas

Ezekiel and Israel’s Legal Traditions

2020 ◽  
Author(s):  
Michael A. Lyons
Keyword(s):  
Broad Sense ◽  
Legal Traditions ◽  
Similarities And Differences

This chapter discusses the similarities and differences in form, content, and vocabulary between the book of Ezekiel and the commands, motivations, and sanctions in the Pentateuch. It considers how legal traditions in the broad sense—that is, not just “laws,” but also statements about obligation, benefits, and punishments—are used in the book of Ezekiel. The logic of the book is deeply indebted to priestly ideology and its notions of purity and holiness. This chapter also examines the possibility, nature, and direction of dependence, both conceptual and literary, between the book of Ezekiel and Israel’s legal traditions (Deuteronomic, Priestly, and Holiness) that were textualized and incorporated into what became the Pentateuch.

scholarly journals Truth, Discussion, and Free Speech in On Liberty II

Utilitas ◽  
2021 ◽  
pp. 1-12
Author(s):  
Christopher Macleod
Keyword(s):  
Free Speech ◽  
Structural Features ◽  
Broad Sense ◽  
True False

Abstract In this article, I offer a reading of On Liberty II which focuses on the structural features of the argument that Mill presents. Mill's argument, I suggest, is grounded on an appeal to the value of truth, and is divided into three sub-arguments, treating true, false and partially true opinion respectively. In section 1, I consider what constraints the teleological orientation of Mill's argument places on the case he makes, before examining in section 2 what the division of Mill's argument into three exhaustive sub-arguments tells us about the nature of ‘discussion’ as Mill uses the term. I go on, in section 3, to suggest that although On Liberty II does not offer a defence of free speech in the broad sense in which the term is often now used, we should be optimistic about the chances of finding such a defence in On Liberty III.

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