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.

Sister (band)

Sister was an American heavy metal band, formed in 1976 in Los Angeles. Former members included Blackie Lawless, formerly of the New York Dolls and later of W.A.S.P., and Nikki Sixx, who would later co-create Mötley Crüe. They are notable for being one of the first bands to make usage of the pentagram and other occult symbols. Due to the late 70's music scene, and personal differences, they never achieved success and broke up sometime in 1978. Sixx and guitarist Lizzie Grey later formed the band London.

Band members

References

Sister (Marbell album)

Sister is the debut album by Japanese alternative rock band Marbell. It was released in Japan on May 14, 2008. The album is Marbell's solitary release as they officially disbanded in March 2010. Music videos were produced for "Miss All Birthday" and "Te no Naru Kata e".

Track listing

References

Sister (Sister2Sister song)

"Sister" was the debut single by Australian pop music duo Sister2Sister. The single was very successful in Australia.

Track listings

In Australia, a remix CD was released.

Charts

In Australia, the single was a huge success. It debuted on the ARIA singles chart at #14, then after several weeks climbed inside the top 10; it peaked at #3 on 12 December 1999. It then slowly fell out of the top 50, and spent a total of 20 weeks inside the top 50.

In New Zealand, the single debuted on the RIANZ singles chart at #14 and fell out quickly, spending eight weeks in the top 50. Two weeks after leaving the top 50, it re-entered at #26, and would fall and rise for a further five weeks before exiting for the last time, bringing its week total to 14.

In the UK, "Sister" debuted at #18, before falling 17 places the next week. It spent two more weeks in the top 100, bringing its total weeks to 4.