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.

Korn

Korn (stylized as KoЯn) is an American nu metal band from Bakersfield, California, formed in 1993. The band's current lineup includes founding members Jonathan Davis (vocals, bagpipes), James "Munky" Shaffer (guitar), Brian "Head" Welch (guitar, backing vocals), and Reginald "Fieldy" Arvizu (bass), with the addition of Ray Luzier (drums), who replaced the band's original member, David Silveria in 2007. Korn was originally formed by three of the members of the band L.A.P.D.

Korn released their first demo album, Neidermayer's Mind, in 1993. The band later went on to release their self-titled debut album in 1994, followed by Life Is Peachy in 1996. The band experienced mainstream success with Follow the Leader (1998) and Issues (1999), both of which debuted at number one on the Billboard 200. The band's mainstream success continued with Untouchables (2002), Take a Look in the Mirror (2003) and See You on the Other Side (2005).

A compilation album, Greatest Hits Vol. 1, was released in 2004, spanning a decade of singles and concluding the band's recording contract with Immortal Records and Epic Records. They signed to Virgin Records, releasing See You on the Other Side in 2005, and an untitled album in 2007. Korn's other recent albums, Korn III: Remember Who You Are (2010) and The Path of Totality (2011), were released via Roadrunner Records, with the latest album The Paradigm Shift (2013) being released via Prospect Park and Caroline Records.

Korn (liquor)

Korn (from German, "grain") is a German colorless distilled beverage that is usually made from fermented rye but may also be made from barley or wheat. Korn differs from vodka in that it is distilled to lower alcoholic proofs and less rigorously filtered, which leaves more of the cereal taste in the finished spirit.

Korn is the cheapest kind of liquor available in northern Germany. It is very popular there and is regarded as the liquor of the working class. In parts of southern Germany, inexpensive fruit brandies (Obstler made from apples, pears, or plums) are more popular.

Traditional Korn contains at least 32% ABV (64 proof). Kornbrand (also called Doppelkorn or Edelkorn) must contain at least 37.5% ABV (75 proof). A weaker variety of Korn that has less than 30% ABV can be a mixture of fruit flavoring and Korn.

The common nickname Klarer (“clear one”) refers to Korn being a clear liquid. Klarer may refer to either Korn or Doppelkorn; the term is sometimes used to market cheap spirits that are weaker (28–30% ABV) than the minimum permitted for Korn.