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.

Nature

Nature, in the broadest sense, is the natural, physical, or material world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large part of science. Although humans are part of nature, human activity is often understood as a separate category from other natural phenomena.

The word nature is derived from the Latin word natura, or "essential qualities, innate disposition", and in ancient times, literally meant "birth".Natura is a Latin translation of the Greek word physis (φύσις), which originally related to the intrinsic characteristics that plants, animals, and other features of the world develop of their own accord. The concept of nature as a whole, the physical universe, is one of several expansions of the original notion; it began with certain core applications of the word φύσις by pre-Socratic philosophers, and has steadily gained currency ever since. This usage continued during the advent of modern scientific method in the last several centuries.

Nature (philosophy)

Nature is a concept with two major sets of inter-related meanings, referring on the one hand to the things which are natural, or subject to the normal working of "laws of nature", or on the other hand to the essential properties and causes of those things to be what they naturally are, or in other words the laws of nature themselves.

How to understand the meaning and significance of nature has been a consistent theme of discussion within the history of Western Civilization, in the philosophical fields of metaphysics and epistemology, as well as in theology and science. The study of natural things and the regular laws which seem to govern them, as opposed to discussion about what it means to be natural, is the area of natural science.

The word "nature" derives from Latin nātūra, a philosophical term derived from the verb for birth, which was used as a translation for the earlier Ancient Greek term phusis which was derived from the verb for natural growth, for example that of a plant. Already in classical times, philosophical use of these words combined two related meanings which have in common that they refer to the way in which things happen by themselves, "naturally", without "interference" from human deliberation, divine intervention, or anything outside of what is considered normal for the natural things being considered.

Gewürztraminer

Gewürztraminer [ɡəˈvʏɐtstʁaˈmiːnɐ]^[p] is an aromatic wine grape variety, used in white wines, and performs best in cooler climates. In English, it is sometimes referred to colloquially as Gewürz (this is never the case in German, because "Gewürz" means "herb" or "spice"), and in French it is written Gewurztraminer (without the umlaut). Gewürztraminer is a variety with a pink to red skin colour, which makes it a "white wine grape" as opposed to the blue to black-skinned varieties commonly referred to as "red wine grapes". The variety has high natural sugar and the wines are white and usually off-dry, with a flamboyant bouquet of lychees. Indeed, Gewürztraminer and lychees share the same aroma compounds. Dry Gewürztraminers may also have aromas of roses, passion fruit and floral notes. It is not uncommon to notice some spritz (fine bubbles on the inside of the glass).

Gewürztraminer's sweetness may offset the spice in Asian cuisine. It goes well with Hirtenkäse,Münster cheese, and fleshy, fatty (oily) wild game.