* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

* Every representable functor C → Set preserves limits ( but not necessarily colimits ).

Every adjunction 〈 F, G, ε, η 〉 gives rise to an associated monad 〈 T, η, μ 〉 in the category D. The functor

Every functor F: D → E induces a functor F < sup > C </ sup >: D < sup > C </ sup > → E < sup > C </ sup > ( by composition with F ).

Every closed category has a forgetful functor to the category of sets, which in particular takes the internal hom to the external hom.

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

Every homomorphism f: G → H of Lie groups induces a homomorphism between the corresponding Lie algebras and.

Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:

Every vector space V with seminorm p ( v ) induces a normed space V / W, called the quotient space, where W is the subspace of V consisting of all vectors v in V with p ( v )

Every correspondence prescription between phase space and Hilbert space, however, induces its own proper-product.

Every note on the scale she screams induces a different effect upon those who hear it.

Every norm induces a prewellordering ; if is a norm, the associated prewellordering is given by

Every stereogenic center in one has the opposite configuration in the other.

The convention details ( amongst other things ) that " Every driver shall keep to the edge of the carriageway appropriate to the direction of traffic ", and the " Drivers overtaking shall do so on the side opposite to that appropriate to the direction of traffic ", notwithstanding the presence or absence of oncoming traffic.

:" Every group is naturally isomorphic to its opposite group "

Every study has found that instead of people's MBTI scores clustering around two opposite poles, such as intuition vs. sensation, with few people scoring in the middle, people's scores actually cluster around the middle of each scale in a bell curve.

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.

Every member of one residency always had an exact mirror opposite number on the other side he could consult with.

Every other Tuesday on the weeks opposite the Clayton Chapel Singing, Xi Chi Delta hosts campus-wide raquetball singings in the Sports Center at 11: 00 pm.

Every gentleman sets as long as he likes to the opposite lady, and the opposite lady to him, and all are so long about it that the sport begins to languish, when suddenly the lively hero dashes in to the rescue.

Every triangle has exactly three medians: one running from each vertex to the opposite side.

Every force (' action ') on one object is accompanied by a ' reaction ' on another, of equal magnitude but opposite direction.

Every morning a bell would ring before dawn so that young couples could get back to rooms so as not to get caught fraternising with the opposite sex.

The first paragraph of article 40, in the current Congolese constitution, states that " Every individual has the right to marry the person of their choice, of the opposite sex ".

Every line through the origin pierces the sphere in two opposite points called antipodes.

Every convex centrally symmetric polyhedron P in R < sup > 3 </ sup > admits a pair of opposite ( antipodal ) points and a path of length L joining them and lying on the boundary ∂ P of P, satisfying

At the insistence of Grant, Drake was subsequently signed to a film contract by RKO Pictures and David Selznick, where she appeared, opposite Grant, in her first film, the romantic comedy Every Girl Should Be Married ( 1948 ).

Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

Every night they all went to Mama and Papa Albright's, and sat on the open front porch, where they could get the breeze.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

Every person should be identified uniquely as resident in one place but where they happen to be on census day, their de facto residence, may not be the best place to count them.

Every SE must be registered in the State where it has its registered office, in a register designated by the law of that State.

Every citation he found described an encounter between males where one party, the master, physically abused another, the slave.

Every ketose will have 2 < sup >( n-3 )</ sup > stereoisomers where n > 2 is the number of carbons.

Every aldose will have 2 < sup >( n-2 )</ sup > stereoisomers where n > 2 is the number of carbons.

Every year, there are growing numbers of regional, national and international wrestling fan conventions, where fans can meet and converse with wrestlers and each other.

In Australia, where Robyn reached the top ten of the iTunes Store's album chart, " With Every Heartbeat " received substantial attention on radio and video networks in Australia.

Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix.

Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.

Every stanza ends with a reference to Canada as the land " where colored men are free ".

Every island has one or two short airstrips where Vanair ’ s Twin Otter planes land two or three times weekly.

Every Saturday morning it hosts a large outdoor market or " mercadillo ", where many gypsies come and sell their wares of fruits and vegetables, clothes and shoes, and other odds and ends.

Every effort was to be made to induce the British to reinforce their forward positions, where the German artillery could engage them.

Every year they would organise an annual meeting, as well as four other academic meetings, where they discussed their research.

Every natural hollow is full of water, around the margin of which, long grasses, reeds and other aquatic plants grow in the greatest profusion, often making it difficult to say where the land ends and the water begins.

Every Easter Monday the doge headed a procession from San Marco to the convent of San Zaccaria where the abbess presented him a new camauro crafted by the nuns.

# Every satisfiable set of formulas is consistent, where a set of formulas is satisfiable if and only if there exists a model such that.

The directive declared, " Every military commander has the responsibility to oppose discriminatory practices affecting his men and their dependents and to foster equal opportunity for them, not only in areas under his immediate control, but also in nearby communities where they may live or gather in off-duty hours.

Every physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator.