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.

Seafood (film)

Seafood (simplified Chinese: 海鲜; traditional Chinese: 海鮮; pinyin: Hǎixiān) is a 2001 Chinese film directed by the established writer Zhu Wen. Though Seafood was Zhu's first film as director, he had already gained some experience with filmmaking as a screenwriter for Zhang Ming (in 1996's Rain Clouds over Wushan) and Zhang Yuan (in 1999's Seventeen Years). Seafood was produced independently by Thought Dance Entertainment and Zhu's own Zhu Wen Workshop.

The film depicts a self-destructive prostitute (Jin Ze) who attempts to commit suicide in a resort town by the sea. She is thwarted by a police officer (Cheng Taisheng) whose unorthodox methods of "rehabilitating" her consists of seafood and rape. As a result of the film's dark premise, Seafood has been called "one of the most transgressive visions of China...ever witnessed."

Never released in China, the film nevertheless was well received abroad, where it won numerous awards most notably at the 2001 Venice International Film Festival.