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.

Knife

A knife (plural knives) is a tool with a cutting edge or blade, hand-held or otherwise, with most having a handle. Some types of knives are used as utensils, including knives used at the dining table (e.g., butter knives and steak knives) and knives used in the kitchen (e.g., paring knife, bread knife, cleaver). Many types of knives are used as tools, such as the utility knife carried by soldiers, the pocket knife carried by hikers and the hunting knife used by hunters. Knives are also used as a traditional or religious implement, such as the kirpan. Some types of knives are used as weapons, such as the daggers used by commandos or the switchblades used by 1950s-era criminal gang members. Some types of knives are used as sports equipment (e.g., throwing knives).

Knife-like tools were used at least two-and-a-half million years ago, as evidenced by the Oldowan tools. Originally made of rock, bone, flint, and obsidian, knives have evolved in construction as technology has, with blades being made from bronze, copper, iron, steel, ceramics, and titanium. Many cultures have their unique version of the knife. Due to its role as humankind's first tool, certain cultures have attached spiritual and religious significance to the knife.

Knives (Babylon 5)

"Knives" is an episode from the second season of the science fiction television series Babylon 5.

Synopsis

Londo Mollari reunites with an old friend, Urza Jaddo. Urza knows that soon he and his house will be declared enemy of the Republic and asks Londo to help him and his family. Londo talks to Lord Refa and asks him not to prosecute Urza. However, when Urza realises that, he becomes angry: it was Refa who ordered Urza's prosecution. Urza challenges Londo to the Morago, a ritual combat using Coutari, Centauri swords. Londo accepts the challenge, even though he could never beat Urza with the Coutari, because refusal would bring disgrace on his family. In the fight Mollari kills Jaddo and feels remorse for it. Later, Vir tries to console him by telling him that Urza would have killed him. Londo explains that Urza could have killed him at any time, but killing Londo would not have helped his family. In defeating Urza in the Morago, Londo must take Urza's family as part of his own. Because they are now House Mollari, the resolution against house Jaddo cannot harm them.