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

Every functor induces the opposite functor, where and are the opposite categories to and.

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 character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

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 ).

Also among the early 32 members were syndicated panel cartoonists Dave Breger ( Mister Breger ), George Clark ( The Neighbors ), Bob Dunn ( Just the Type ) and Jimmy Hatlo ( They'll Do It Every Time ); freelance magazine cartoonists Abner Dean and Mischa Richter, editorial cartoonists Rube Goldberg ( New York Sun ), Burris Jenkins ( New York Journal American ), C. D. Batchelor ( Daily News ) and Richard Q. Yardley ( The Baltimore Sun ); sports cartoonist Lou Hanlon ; illustrator Russell Patterson and comic book artists Joe Shuster and Joe Musial.

* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.

Every year since 1982, the W. C. Handy Music Festival is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and R & B.

According to Canon C. 24, " Every priest having a cure of souls shall provide that, in the absence of reasonable hindrance, Morning and Evening Prayer daily and on appointed days the Litany shall be said in the church, or one of the churches, of which he is the minister.

" Canon C. 26 stipulates that " Every clerk ( cleric ) in Holy Orders is under obligation, not being let ( prevented ) by sickness or some other urgent cause, to say daily the Morning and Evening Prayer ...." In other Anglican provinces, the Daily Office is not a canonical obligation but is strongly encouraged.

Every algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic map of C into J.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

Every state on a C *- algebra is of the above type.

Every fall, FRC Action ( the political action group affiliated with FRC ) holds an annual summit composed for conservative Christian activists and evangelical voters in Washington, D. C.

Every year, dozens of graduates go on to elite colleges, and T. C.

This means that A is not necessarily better than B, and B is not necessarily better than C. Every class is independent of the others.

* Every finite-dimensional simple algebra over R must be a matrix ring over R, C, or H. Every central simple algebra over R must be a matrix ring over R or H. These results follow from the Frobenius theorem.

* Every finite-dimensional simple algebra over C must be a matrix ring over C and hence every central simple algebra over C must be a matrix ring over C.

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 universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.

Every Boolean algebra is a Heyting algebra when a → b is defined as usual as ¬ a ∨ b, as is every complete distributive lattice when a → b is taken to be the supremum of the set of all c for which a ∧ c ≤ b. The open sets of a topological space form a complete distributive lattice and hence a Heyting algebra.

* Every continuous function f: → R is bounded.

Every morphism f: G → H in Grp has a category-theoretic kernel ( given by the ordinary kernel of algebra ker f =

Every isogeny f: A → B is automatically a group homomorphism between the groups of k-valued points of A and B, for any field k over which f is defined.

# Every subset of an independent set is independent, i. e., for each E ' ⊆ E, E ∈ I → E ' ∈ I.

They created memorable videos for The Police (" Every Breath You Take ", " Synchronicity II ", " Wrapped Around Your Finger "), Duran Duran (" Girls on Film ", " A View to a Kill "), Herbie Hancock (" Rockit "), Go West (" We Close Our Eyes "), Frankie Goes to Hollywood (" Two Tribes ", " The Power of Love "), Sting (" If You Love Somebody Set Them Free " " Fields of Gold "), and Wang Chung (" Everybody Have Fun Tonight "), among many others, up to Godley's video for the 1996 single from The Beatles, " Real Love ", featured in the Beatles Anthology.

* Sting ( introduced by Harry Belafonte ) – " If You Love Somebody Set Them Free ", " They Dance Alone ", " Every Breath You Take ", " Message in a Bottle "

Every five years, OFWAT set limits on the prices which UK water companies can charge to their customers ; this process is known as a Price Review.

Every aircraft type has limits on the pitch-power settings that can be used for climbing flight.

Every feature on every manufactured part is subject to variation, therefore, the limits of allowable variation must be specified.

Every publishing company that had printed it was closed and sealed, diocesan newspapers were proscribed, and limits imposed on the paper available for Church purposes.

Every other interchange with major roads along the route ( Toorak, Burke, Tooronga and Warrigal Roads ) was an at-grade intersection controlled by traffic-lights, and because the road was constructed through residential areas, reduced speed limits were also enforced.

Every day, there are more than one million vehicles travelling within the city limits.

Every eligible voter may join or lead one political party provided they are not disqualified by other law ; political parties meanwhile operate under their charters within the limits and requirements of the Election Act.

According to Article 3 of the 1922 Constitution of the Irish Free State, " Every person, without distinction of sex, domiciled in the area of the jurisdiction of the Irish Free State ( Saorstát Eireann ) at the time of the coming into operation of this Constitution who was born in Ireland or either of whose parents was born in Ireland or who has been ordinarily resident in the area of the jurisdiction of the Irish Free State ( Saorstát Eireann ) for not less than seven years, is a citizen of the Irish Free State ( Saorstát Eireann ) and shall within the limits of the jurisdiction of the Irish Free State ( Saorstát Eireann ) enjoy the privileges and be subject to the obligations of such citizenship [...]".

Every heat engine is subject to the theoretical efficiency limits of the Carnot cycle.

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 morphism in a concrete category whose underlying function is injective is a monomorphism ; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.

Every composite number can be written as the product of two or more ( not necessarily distinct ) primes ; furthermore, this representation is unique up to the order of the factors.

Every railway seemed to have its own idea of car design, and ready-made cars would necessarily be of Ohio Falls ’ design.

Every association of men is necessarily a separation from other men ... the political thus understood is not the constitutive principle of the state, of order, but a condition of the state.

Every cognition implies necessarily a judgment, but not every judgment is necessarily cognition, because there are also judgments that are not true.

Every association of men is necessarily a separation from other men ... the political thus understood is not the constitutive principle of the state, of order, but a condition of the state.

Every imperfect field is necessarily transcendental over its prime subfield ( the minimal subfield ), because the latter is perfect.

* Every relation in L ( R ) can be uniformized, but not necessarily by a function in L ( R ).

" He continues: " Every category ... every description of existence or relation, is necessarily a transcript from our own nature and our own experience.