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
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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."
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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."
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Order as a noun (countable):
Arrangement, disposition, or sequence.
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Order as a noun (countable):
A position in an arrangement, disposition, or sequence.
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Order as a noun (uncountable):
The state of being well arranged.
Examples:
"The house is in order; the machinery is out of order."
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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"
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Order as a noun (countable):
A command.
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Order as a noun (countable):
A request for some product or service; a commission to purchase, sell, or supply goods.
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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."
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Order as a noun (countable):
An association of knights
Examples:
"the Order of the Garter, the Order of the Bath."
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Order as a noun:
any group of people with common interests.
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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.
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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."
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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"
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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"
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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.
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Order as a noun (cricket):
The sequence in which a side's batsmen bat; the batting order.
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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."
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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.
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Order as a noun (set theory):
The cardinality, or number of elements in a set, group, or other structure regardable as a set.
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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).
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Order as a noun (graph theory):
The number of vertices in a graph.
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Order as a noun (order theory):
A partially ordered set.
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Order as a noun (order theory):
The relation on a partially ordered set that determines that it is, in fact, a partially ordered set.
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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."
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Order as a verb (transitive):
To set in some sort of order.
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Order as a verb (transitive):
To arrange, set in proper order.
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Order as a verb (transitive):
To issue a command to.
Examples:
"to order troops to advance"
"He ordered me to leave."
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Order as a verb (transitive):
To request some product or service; to secure by placing an order.
Examples:
"to order groceries"
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Order as a verb:
To admit to holy orders; to ordain; to receive into the ranks of the ministry.