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

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## Some Related Sentences

Every and continuous

__Every__character is automatically

__continuous__from A to C, since

**the**kernel of

**a**character is

**a**maximal ideal,

**which**is closed.

*****

__Every__

__continuous__map from

**a**compact space to

**a**Hausdorff space is closed and proper

**(**i. e.,

**the**pre-image of

**a**compact

**set**is compact.

__Every__contraction mapping is Lipschitz

__continuous__and hence uniformly

__continuous__

**(**for

**a**Lipschitz

__continuous__function,

**the**constant k is no longer necessarily less than 1

**).**

__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__separable metric space is isometric to

**a**subset of C (),

**the**separable Banach space of

__continuous__functions → R, with

**the**supremum norm.

__Every__topological group can be viewed as

**a**uniform space in two ways ;

**the**left uniformity turns all left multiplications into uniformly

__continuous__maps while

**the**right uniformity turns all right multiplications into uniformly

__continuous__maps.

__Every__

__continuous__function in

**the**function space can be represented as

**a**linear combination of basis functions, just as every vector in

**a**vector space can be represented as

**a**linear combination of basis vectors.

__Every__map that is injective,

__continuous__and either open or closed is an embedding ; however there are also embeddings

**which**are neither open nor closed.

*****

__Every__compact Hausdorff space of weight at most

**(**see Aleph number ) is

**the**

__continuous__image of

**(**this does not need

**the**continuum hypothesis, but is less interesting in its absence

**).**

__Every__place south of

**the**Antarctic Circle experiences

**a**period of twenty-four hours '

__continuous__daylight at least once per year, and

**a**period of twenty-four hours '

__continuous__night time at least once per year.

Every and functor

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__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 and on

__Every__day, when

**the**President took his nap, Rob Roy would stretch out

__on__

**the**window seat near him, like

**a**perfect gentleman, and stare thoughtfully out

**the**window, or he would take

**a**little nap himself.

__Every__man who dabbles in

**the**market to make

**a**little easy money

__on__

**the**side and suffers losses could at

**the**time hardly face his wife who was wondering how her husband could be so dumb.

__Every__few minutes she would awaken for

**a**moment to review things: Stowey, yes, was

__on__his way south, and

**the**two boys were away in school, and nothing was burning

__on__

**the**stove, and Lucretia was coming for dinner and bringing three guests of hers.

__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__few days, in

**the**early morning, as

**the**work progressed, twenty men would appear to push it ahead and to shift

**the**plank foundation that distributed its weight widely

__on__

**the**Rotunda pavement, supported as it is by ancient brick vaulting.

__Every__night when he wanted

**a**drink of water, didn't he practice being fearless by not turning

__on__

**the**bathroom light??

__Every__single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors

__on__average increased inclusive fitness in

**the**ancestral environment.

__Every__year,

__on__

**the**last Sunday in April, there is an ice fishing competition in

**the**frozen estuarine waters of

**the**Anadyr River's mouth.

__Every__actor who

**has**opened in

**the**role of Pseudolus

__on__Broadway

**(**Zero Mostel, Phil Silvers and Nathan Lane ) won

**a**Best Actor Tony Award for their performance.

*****Revised Code of Washington 9. 12. 010: "

__Every__person who brings

__on__his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass

**a**defendant in

**the**suit, or who serves or sends any paper or document purporting to be or resembling

**a**judicial process, that is not in fact

**a**judicial process, is guilty of

**a**misdemeanor ; and in case

**the**person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.

__Every__year,

**the**European Joint Conferences

__on__Theory and Practice of Software

**(**ETAPS ) sponsors

**the**International Conference

__on__Compiler Construction

**(**CC ), with papers from both

**the**academic and industrial sectors.

__Every__Halloween, Dabney House conducts

**the**infamous " Millikan pumpkin-drop experiment " from

**the**top of Millikan Library,

**the**highest point

__on__campus.

__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.

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