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.

Leprechaun (1982 video game)

Leprechaun (レプリカン, Repurikan) is an arcade game manufactured by Tong Electronic Inc. in 1982. It was also manufactured as Pot of Gold by Game Plan Inc. Currently, there are only four known machines of Leprechaun and nine known Pot of Gold machines, though only four are fully intact.

Gameplay

The player controls a sleuth running through a forest, trying to get a Leprechaun's pot of gold. The pot of gold is randomly placed on the screen. When the pot of gold is touched, the player is taken to the next level. The Leprechaun chases the sleuth through the forest, trying to catch him. If he is caught the player loses a life and starts over from the beginning of the level. After all lives are lost, the game ends. Should the Leprechaun reach the pot of gold first, it is then relocated to another place on the screen. By touching the trees, the player's score increases, as does the value of the pot of gold. Every time the Leprechaun touches a tree, the pot's value decreases though the player's score remains the same. After each level and after every 30 seconds the Leprechaun's speed increases.

Leprechaun 3

Leprechaun 3 is a 1995 American comedy fantasy horror film. It is the third installment and first direct-to-video entry in the Leprechaun series.

Plot

After being pawned to a Las Vegas shop owner, Gupta, the Leprechaun (Davis) jumps on his back and bites off a part of his ear, accusing him of being a greedy thief. He then beats the Gupta's legs with his walking stick and notices that he's wearing leather shoes. He removes one and states that he "appreciates a good pair of shoes." He looks down and notices Gupta's sock has a hole in it, revealing his big toe. The Leprechaun takes a hold of his foot and says, "Ah, don't mind if I do!", and then proceeds to bite the man's big toe off. Before he can cause him anymore harm, Gupta reveals that he is wearing a medallion that he found on the Leprechaun's then petrified body. The Leprechaun runs from it and hides in the basement, where Gupta follows him and is shot in the arm with an arrow from a Cupid statue. He runs back upstairs to call for help, but is strangled to death by the Leprechaun via the phone cord. He is found by college student, Scott McCoy, who has fallen for a casino employee named Tammy Larsen. Scott steals Leprechaun’s coin which in this movie has the ability to grant one wish per person. This one wish can do Leprechaun no harm. This is also the first movie in which Leprechaun can be turned into concrete if forced to wear a medallion.

Leprechaun: Back 2 tha Hood

Leprechaun: Back 2 tha Hood is a 2003 American direct-to-video comedy horror film written and directed by Steven Ayromlooi. It is the sixth installment of the Leprechaun , and as of 2015, the last entry to star Warwick Davis in the titular role. The film has the villainous Leprechaun rampaging through a town looking for his gold, which was stolen by a group of urban youths who are using it to fulfill their wildest dreams. He will hunt and kill to retrieve his pot of gold.

Plot

The film opens with an animated prologue revealing the origins of leprechauns, stating that they were summoned by a king to protect his gold. After the death of the king the Leprechauns returned to their places of origin, all except one (Warwick Davis) who through the ages slowly became corrupted and obsessed with the gold he still guarded. In the year 2000, Father Jacob (Willie C. Carpenter) finds the leprechaun's gold and intends to build a youth center. Jacob manages to banish Lubdan the Leprechaun, summoning demonic hands which drag him underground, but soon after dies of injuries inflicted by the leprechaun during the fight.