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Category vs Characteristic - What's the difference?

category | characteristic |

In mathematics terms the difference between category and characteristic

is that 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 while characteristic is the integer part of a logarithm.

As nouns the difference between category and characteristic

is that category is a group, often named or numbered, to which items are assigned based on similarity or defined criteria while characteristic is a distinguishable feature of a person or thing.

As an adjective characteristic is

being a distinguishing feature of a person or thing.

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

    characteristic

    Adjective

    (en adjective)
  • Being a distinguishing feature of a person or thing.
  • * , chapter=12
  • , title= The Mirror and the Lamp , passage=All this was extraordinarily distasteful to Churchill. It was ugly, gross. Never before had he felt such repulsion when the vicar displayed his characteristic bluntness or coarseness of speech. In the present connexion […] such talk had been distressingly out of place.}}

    Synonyms

    * distinctive * exclusive * idiosyncratic * indicative * representative * signature * specific * typical

    Antonyms

    * uncharacteristic * untypical

    Derived terms

    * characteristic function * characteristicness

    Noun

    (en noun)
  • a distinguishable feature of a person or thing
  • (mathematics) the integer part of a logarithm
  • (nautical) the distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc)
  • (algebra, field theory) The minimum number of times that the unit of a field must be added unto itself in order to yield that field's zero, or, if that minimum natural number does not exist, then (the integer) zero.
  • A field's characteristic, if non-zero, must be a prime number.

    Synonyms

    * attribute * idiosyncrasy * mannerism * quality * tendency * trademark * trait * See also

    Derived terms

    * defining characteristic

    See also

    * mantissa