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.

Goat

The domestic goat (Capra aegagrus hircus) is a subspecies of goat domesticated from the wild goat of southwest Asia and Eastern Europe.

The goat is a member of the family Bovidae and is closely related to the sheep as both are in the goat-antelope subfamily Caprinae. There are over 300 distinct breeds of goat. Goats are one of the oldest domesticated species, and have been used for their milk, meat, hair, and skins over much of the world. In 2011, there were more than 924 million live goats around the globe, according to the UN Food and Agriculture Organization.

Female goats are referred to as "does" or "nannies", intact males as "bucks", "billies", or "rams" and their offspring are "kids". Castrated males are "wethers". Goat meat from younger animals is called "kid" or cabrito (Spanish), and from older animals is simply known as "goat" or sometimes called chevon (French), or in some areas "mutton" (which more often refers to adult sheep meat).

Etymology

The Modern English word goat comes from Old English gāt "she-goat, goat in general", which in turn derives from Proto-Germanic *gaitaz (cf. Dutch/Icelandic geit, German Geiß, and Gothic gaits), ultimately from Proto-Indo-European *ǵʰaidos meaning "young goat" (cf. Latin haedus "kid"), itself perhaps from a root meaning "jump" (assuming that Old Church Slavonic zajęcǐ "hare", Sanskrit jihīte "he moves" are related). To refer to the male, Old English used bucca (giving modern buck) until ousted by hegote, hegoote in the late 12th century. Nanny goat (females) originated in the 18th century and billy goat (for males) in the 19th.

Goat (band)

Goat is a Swedish alternative and experimental fusion music group. The band originates—according to its own publicity—from Korpilombolo, Norrbotten County, Sweden. Their album World Music, released on 20 August 2012 by Rocket Recordings, was hailed by The Guardian as one of the best albums of 2012.

History

Formation

Goat, though currently based in Gothenburg, claims to hail from Korpilombolo in Sweden which, according to the band's own publicity, has a history of voodoo worship after a witch doctor came and lived there. Supposedly, when Christian crusaders came and destroyed the village the surviving people fled and placed a curse on the town. This has been described as "a lovely story, if possibly not entirely rooted in reality."

The band started playing music when they were children, as part of a local community tradition, and there have been many incarnations of Goat who have recorded over the last "30 or 40 years". There are now three original "core" members of the band, from Korpilombolo, but in live concerts they are augmented by four other performers from Gothenburg.

Goat (zodiac)

The Goat (Chinese: 羊; pinyin: yáng) is the eighth sign of the 12-year cycle of animals that appear in the Chinese zodiac related to the Chinese calendar. The sign is also referred to as the Ram or Sheep sign, since the Chinese word yáng is more accurately translated as Caprinae, a taxonomic subfamily which includes both sheep and goats.

The Year of the Goat (alternatively, Year of the Ram or Year of the Sheep) is associated with the 8th Earthly Branch symbol, 未 (wèi).

Goat or Sheep

The Chinese word yáng refers both to goats and sheep, with shānyáng specifically goats and miányáng sheep. In English, the sign (originally based on a horned animal) may be called either. The interpretation of sheep or goat depends on culture. In Vietnamese, the sign is mùi, which is unambiguously goat. In Japan, on the other hand, the sign is hitsuji, sheep; while in Korea and Mongolia the sign is also sheep or ram. Within China, there may be a regional distinction with the zodiacal yáng more likely to be thought of as a goat in the south, while tending to be thought of as a sheep in the north.