The difference between Category and Order

When used as nouns, category means a group, often named or numbered, to which items are assigned based on similarity or defined criteria, whereas order means arrangement, disposition, or sequence.


Order is also verb with the meaning: to set in some sort of order.

check bellow for the other definitions of Category and Order

  1. Category as a noun:

    A group, often named or numbered, to which items are assigned based on similarity or defined criteria.

    Examples:

    "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."

  2. Category as a noun (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.

    Examples:

    "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."

  1. Order as a noun (countable):

    Arrangement, disposition, or sequence.

  2. Order as a noun (countable):

    A position in an arrangement, disposition, or sequence.

  3. Order as a noun (uncountable):

    The state of being well arranged.

    Examples:

    "The house is in order; the machinery is out of order."

  4. Order as a noun (countable):

    Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet.

    Examples:

    "to preserve order in a community or an assembly"

  5. Order as a noun (countable):

    A command.

  6. Order as a noun (countable):

    A request for some product or service; a commission to purchase, sell, or supply goods.

  7. Order as a noun (countable):

    A group of religious adherents, especially monks or nuns, set apart within their religion by adherence to a particular rule or set of principles

    Examples:

    "St. Ignatius Loyola founded the Jesuit order in 1537."

  8. Order as a noun (countable):

    An association of knights

    Examples:

    "the Order of the Garter, the Order of the Bath."

  9. Order as a noun:

    any group of people with common interests.

  10. Order as a noun (countable):

    A decoration, awarded by a government, a dynastic house, or a religious body to an individual, usually for distinguished service to a nation or to humanity.

  11. Order as a noun (countable, taxonomy):

    A rank in the classification of organisms, below class and above family; a taxon at that rank.

    Examples:

    "Magnolias belong to the order Magnoliales."

  12. Order as a noun:

    A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a distinct character, kind, or sort.

    Examples:

    "the higher or lower orders of society"

    "talent of a high order"

  13. Order as a noun:

    An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; often used in the plural.

    Examples:

    "to take orders, or to take holy orders, that is, to enter some grade of the ministry"

  14. Order as a noun (architecture):

    The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (as the column and entablature are the characteristic features of classical architecture) a style or manner of architectural designing.

  15. Order as a noun (cricket):

    The sequence in which a side's batsmen bat; the batting order.

  16. Order as a noun (electronics):

    a power of polynomial function in an electronic circuit's block, such as a filter, an amplifier, etc.

    Examples:

    "a 3-stage cascade of a 2nd-order bandpass Butterworth filter."

  17. Order as a noun (chemistry):

    The overall power of the rate law of a chemical reaction, expressed as a polynomial function of concentrations of reactants and products.

  18. Order as a noun (set theory):

    The cardinality, or number of elements in a set, group, or other structure regardable as a set.

  19. Order as a noun (group theory, of an element of a group):

    For given group G and element g ∈ G, the smallest positive natural number n, if it exists, such that (using multiplicative notation), gn = e, where e is the identity element of G; if no such number exists, the element is said to be of infinite order (or sometimes zero order).

  20. Order as a noun (graph theory):

    The number of vertices in a graph.

  21. Order as a noun (order theory):

    A partially ordered set.

  22. Order as a noun (order theory):

    The relation on a partially ordered set that determines that it is, in fact, a partially ordered set.

  23. Order as a noun (algebra):

    The sum of the exponents on the variables in a monomial, or the highest such among all monomials in a polynomial.

    Examples:

    "A quadratic polynomial, <math>a x^2 + b x +c,</math> is said to be of order (or degree) 2."

  1. Order as a verb (transitive):

    To set in some sort of order.

  2. Order as a verb (transitive):

    To arrange, set in proper order.

  3. Order as a verb (transitive):

    To issue a command to.

    Examples:

    "to order troops to advance"

    "He ordered me to leave."

  4. Order as a verb (transitive):

    To request some product or service; to secure by placing an order.

    Examples:

    "to order groceries"

  5. Order as a verb:

    To admit to holy orders; to ordain; to receive into the ranks of the ministry.