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Area vs Category - What's the difference?

area | category |

In mathematics terms the difference between area and category

is that area is a measure of the extent of a surface; it is measured in square units while category is a collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.

area

English

Noun

(wikipedia area)
  • (mathematics) A measure of the extent of a surface; it is measured in square units.
  • A particular geographic region.
  • Any particular extent of surface, especially an empty or unused extent.
  • Figuratively, any extent, scope or range of an object or concept.
  • * {{quote-magazine, year=2013, month=September-October, author= Rob Dorit
  • , magazine=(American Scientist), title= Making Life from Scratch , passage=Today, a new area of research that similarly aims to mimic a complex biological phenomenon—life itself—is taking off. Synthetic biology, a seductive experimental subfield in the life sciences, seems tantalizingly to promise custom-designed life created in the laboratory.}}
  • (British) An open space, below ground level, between the front of a house and the pavement.
  • (Charles Dickens)
  • (soccer) Penalty box; penalty area.
  • * {{quote-news, year=2010, date=December 29, author=Mark Vesty, work=BBC
  • , title= Wigan 2-2 Arsenal , passage=Bendtner's goal-bound shot was well saved by goalkeeper Ali Al Habsi but fell to Arsahvin on the edge of the area and the Russian swivelled, shaped his body and angled a sumptuous volley into the corner.}}
  • (slang) Genitals.
  • Derived terms

    * * area code * area-denial * area of influence * area rug * area rule * Broca's area * combined statistical area * common area * danger area * disaster area * equal-area * free trade area * geographical area * goal area * gray area * grey area * lateral area * metropolitan area * metropolitan area network * notification area * outside gross area * penalty area * Planck area * prohibited area * protected area * rest area * restricted area * Ruhr Area * Schengen Area * safe area * second moment of area * service area * specific leaf area * staging area * surface area * terminal control area * Terminal High Altitude Area Defense * ventral tegmental area * Wernicke's area

    See also

    * Imperial: square inches, square feet, square yards, square miles, acres * Metric: square meters/square metres, square centimeters/square centimetres, square kilometers/square kilometres, hectares

    Anagrams

    * 1000 English basic words ----

    category

    Noun

    (categories)
  • A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
  • *
  • The traditional way of describing the similarities and differences between constituents is to say that they belong to categories'' of various types. Thus, words like ''boy'', ''girl'', ''man'', ''woman'', etc. are traditionally said to belong to the category''' of Nouns, whereas words like ''a'', ''the'', ''this'', and ''that'' are traditionally said to belong to the ' category of Determiners.
    This steep and dangerous climb belongs to the most difficult category .
    I wouldn't put this book in the same category as the author's first novel.
  • (mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
  • One well-known category has sets as objects and functions as arrows.
    Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.

    Synonyms

    * (group to which items are assigned) class, family, genus, group, kingdom, order, phylum, race, tribe, type * See also

    Derived terms

    * category mistake * category theory * conceptual category * perceptual category * subcategory * supercategory