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.

Hair (disambiguation)

Hair is a protein filament that grows from follicles in the skin.

Hair may also refer to:

People

Biology

Art, entertainment and media

Music

Musical

Television

Other uses

Hair (Lady Gaga song)

"Hair" is a song recorded by American singer Lady Gaga for her second studio album, Born This Way (2011). Written and produced by Gaga and RedOne, "Hair" was released worldwide digitally on May 16, 2011, as a promotional single from the album, as part of the iTunes Store's "Countdown to Born This Way" release. This was after the previous promotional release, "The Edge of Glory", was made the third single from the album. Nevertheless, Gaga explained that "Hair" was not planned to be a single, but may be released as one if it sells well at the iTunes Store, like "The Edge of Glory".

According to Lady Gaga, the melody of "Hair" resembles the work of metal bands Kiss and Iron Maiden, and is also influenced by Bruce Springsteen. The song is an uptempo club record inspired by Gaga's experience as a teenager, when her parents forced her to dress in a certain way. Gaga found that the only way to express herself was through her hair, and she described it as a song about liberation and her ability to change her ways. The lyrics talk about embracing one's hairstyle as their ultimate expression of freedom. "Hair" was recorded while Gaga was on tour with The Monster Ball throughout Europe. The song features a saxophone solo performed by saxophonist Clarence Clemons, a prominent member of The E Street Band. She personally wanted Clemons to play saxophone on the song, which he did by recording his part at a Manhattan studio at midnight, after he had just flown there from his home in Florida.

Hair (musical)

Hair: The American Tribal Love-Rock Musical is a rock musical with a book and lyrics by James Rado and Gerome Ragni and music by Galt MacDermot. A product of the hippie counterculture and sexual revolution of the 1960s, several of its songs became anthems of the anti-Vietnam War peace movement. The musical's profanity, its depiction of the use of illegal drugs, its treatment of sexuality, its irreverence for the American flag, and its nude scene caused much comment and controversy. The musical broke new ground in musical theatre by defining the genre of "rock musical", using a racially integrated cast, and inviting the audience onstage for a "Be-In" finale.

Hair tells the story of the "tribe", a group of politically active, long-haired hippies of the "Age of Aquarius" living a bohemian life in New York City and fighting against conscription into the Vietnam War. Claude, his good friend Berger, their roommate Sheila and their friends struggle to balance their young lives, loves, and the sexual revolution with their rebellion against the war and their conservative parents and society. Ultimately, Claude must decide whether to resist the draft as his friends have done, or to succumb to the pressures of his parents (and conservative America) to serve in Vietnam, compromising his pacifistic principles and risking his life.