Category

Category, plural categories, may refer to:

Philosophy and general uses

Mathematics

Linguistics

Lusternik–Schnirelmann category

In mathematics, the Lyusternik–Schnirelmann category (or, Lusternik–Schnirelmann category, LS-category) of a topological space is the homotopical invariant defined to be the smallest integer number such that there is an open covering of with the property that each inclusion map is nullhomotopic. For example, if is the circle, this takes the value two.

Sometimes a different normalization of the invariant is adopted, which is one less than the definition above Such a normalization has been adopted in the definitive monograph by Cornea, Lupton, Oprea, and Tanré (see below).

In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems. It has a close connection with algebraic topology, in particular cup-length. In the modern normalization, the cup-length is a lower bound for LS category.

It was, as originally defined for the case of X a manifold, the lower bound for the number of critical points that a real-valued function on X could possess (this should be compared with the result in Morse theory that shows that the sum of the Betti numbers is a lower bound for the number of critical points of a Morse function).

Grammatical category

A grammatical category is a property of items within the grammar of a language; it has a number of possible values (sometimes called grammemes), which are normally mutually exclusive within a given category. Examples of frequently encountered grammatical categories include tense (which may take values such as present, past, etc.), number (with values such as singular, plural, and sometimes dual), and gender (with values such as masculine, feminine and neuter).

Although terminology is not always consistent, a distinction should be made between these grammatical categories (tense, number, etc.) and lexical categories, which are closely synonymous with the traditional parts of speech (noun, verb, adjective, etc.), or more generally syntactic categories. Grammatical categories are also referred to as (grammatical) features.

The name given to a grammatical category (as an uncountable noun) is generally also used (as a countable noun) to denote any of the possible values for that category. For example, the values available in a given language for the category "tense" are called "tenses", the values available for the category "gender" are called "genders", and so on.

Work of art

A work of art, artwork, art piece, piece of art or art object is an aesthetic physical item or artistic creation. Apart from "work of art", which may be used of any work regarded as art in its widest sense, including works from literature and music, these terms apply principally to tangible, portable forms of visual art:

Used more broadly, the term is less commonly applied to:

Works (Pink Floyd album)

Works is a Pink Floyd compilation album released in 1983. It features a variety of material, such as (among others) the band's early singles, "Arnold Layne" and "See Emily Play", alternative mixes of tracks from The Dark Side of the Moon, and the previously unreleased track, "Embryo".

Release and contents

The album was released by their former American label, Capitol Records, to compete with their then-current album The Final Cut. The main interest for collectors is the track "Embryo", an outtake from Ummagumma that later became a concert staple in a greatly elongated form, which originally only appeared in January 1970 on a scarce various artists compilation album promoting Pink Floyd's UK label Harvest Records entitled Picnic – A Breath of Fresh Air. Also unique to Works, the tracks "Brain Damage" and "Eclipse" are presented as alternate versions, possibly stereo mixes from the master tapes of the quadraphonic edition of The Dark Side of the Moon.

Alternate recordings

Factory-backed

In motorsports, a factory-backed racing team or driver is one sponsored by a vehicle manufacturer in official competitions. As motorsport competition is an expensive endeavor, some degree of factory support is desired and often necessary for success. The lowest form of factory backing comes in the form of contingency awards, based upon performance, which help to defray the cost of competing. Full factory backing can be often seen in the highest forms of international competition, with major motorsport operations often receiving hundreds of millions of euros to represent a particular manufacturer.

One-make series can also be backed by the factory, notably Ferrari Challenge and Porsche Supercup purely to allow themselves sell their competition specials of their models to customers and to organize series. These series commonly offer prize money and even sometimes a factory drive to an upper lever series.

In lower level racing, support from dealerships and importers may also be referred to as factory backing. In drifting, where factory backed teams are few and far between (Mopar and Pontiac of Formula D for example), works team/drivers are those backed by large or highly established tuning companies, as opposed to those entered by the drivers themselves or smaller and less well-off tuning companies. The advantage to this is drivers can get access to expensive prototype parts provided by the company that are not yet available to customers and in the event of their car being too badly damaged to compete, a back-up car will be available to them.