For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??

For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;

For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.

For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.

For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;

For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:

For example: 1.

For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.

For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.

For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.

For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;

For example, a 12-to-one engine would power a supersonic VTOL fighter.

For example: Af.

For example: Af.

For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.

For example: Af.

For example, let's consider a standard 283 cubic inch Chevy Aj.

For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.

For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.

For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.

For example, the Friday after Thanksgiving can be substituted for Washington's birthday.

For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.

For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.

For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.

* For any category C and object A of C the Hom functor Hom ( A ,–): C → Set preserves all limits in C. In particular, Hom functors are continuous.

For every object X of C, let Hom (-, X ) be the contravariant representable functor from C to Set.

For example, despite the fact that Asian cuisine had been available in the UK since the 1960s, it was only due to the influence of chefs like Ken Hom and Madhur Jaffrey in the early eighties that the public became aware that these anglicised meals were not the authentic article.

For each object A of C let Hom ( A ,–) be the hom functor which maps objects X to the set Hom ( A, X ).

* For a field k, a finite-dimensional, unital, associative algebra is Frobenius if and only if the injective right A-module Hom < sub > k </ sub >( A, k ) is isomorphic to the right regular representation of A.

For example, for each B-module M, the induced module A ⊗< sub > B </ sub > M ( if M is a left module ) and co-induced module Hom < sub > B </ sub >( A, M ) are naturally isomorphic as A-modules ( as an exercise one defines the isomorphism given E and dual bases ).

Examples of those instrstructures includes: For Railway-the completion of MTR Tseung Kwan O Line in 2002, KCR West Rail in 2003, KCR Ma On Shan Rail in 2004, MTR Disneyland Resort Line in 2005, the extension of the Airport Express to AsiaWorld-Expo in 2005, KCR Lok Ma Chau Spur Line in 2007, and MTR Kowloon Southern Link between East Rail Line and West Rail Line from Hung Hom Station to Nam Cheong Station via East Tsim Sha Tsui Station and Austin Station in 2009.

( For groups of low 2-rank the proof of this breaks down, because theorems such as the signalizer functor theorem only work for groups with elementary abelian subgroups of rank at least 3.

Diagram: For categories C and J, a diagram of type J in C is a covariant functor.

( Category theoretical ) presheaf: For categories C and J, a J-presheaf on C is a contravariant functor.

Limit functor: For a fixed index category J, if every functor J → C has a limit ( for instance if C is complete ), then the limit functor C < sup > J </ sup >→ C assigns to each functor its limit.

For an abelian category C, the inverse limit functor

A functor G is said to preserve all limits of type J if it preserves the limits of all diagrams F: J → C. For example, one can say that G preserves products, equalizers, pullbacks, etc.

For instance, a functor G preserves the colimits of F if G ( L, φ ) is a colimit of GF whenever ( L, φ ) is a colimit of F. A cocontinuous functor is one that preserves all small colimits.

For a given diagram F: J → C and functor G: C → D, if both F and GF have specified limits there is a unique canonical morphism

For contravariant functors the corresponding notions would be a functor that takes colimits to limits, or one that takes limits to colimits.

For a simple example, if the rings R and S are represented by the one-object preadditive categories R and S, then a ring homomorphism from R to S is represented by an additive functor from R to S, and conversely.

For each prime number p, this provides a functor from the category of abelian groups to the category of p-power torsion groups that sends every group to its p-power torsion subgroup, and restricts every homomorphism to the p-torsion subgroups.

For example, " the concrete category Set " means the pair ( Set, I ) where I denotes the identity functor Set → Set.

# For technical reasons, the category Ban < sub > 1 </ sub > of Banach spaces and linear contractions is often equipped not with the " obvious " forgetful functor but the functor U < sub > 1 </ sub >: Ban < sub > 1 </ sub > → Set which maps a Banach space to its ( closed ) unit ball.

For this reason, it makes sense to call a pair ( C, U ) where C is a category and U a faithful functor C → X a concrete category over X.

For the free functor to be a left adjoint, one must also have a Set-morphism.

For example the tensor algebra construction on a vector space as left adjoint to the functor on associative algebras that ignores the algebra structure.

For example, a G-set is equivalent to a functor from G to the category of sets, Set, and a linear representation is equivalent to a functor to the category of vector spaces over a field, Vect < sub > K </ sub >.