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

Every adjunction 〈 F, G, ε, η 〉 extends an equivalence of certain subcategories.

Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).

Every statement in F #, including statements and loops, is a composable expression with a definite return type as well.

Every field has an algebraic closure, and it is unique up to an isomorphism that fixes F.

* Every subextension of F / k is separable.

* Every finite subextension of F / k is separable.

* Every 4-dimensional central simple algebra over a field F is isomorphic to a quaternion algebra ; in fact, it is either a two-by-two matrix algebra, or a division algebra.

* Every reduced commutative k-algebra A is a separable algebra ; i. e., is reduced for every field extension F / k.

President John F. Kennedy said of Hayden, " Every Federal program which has contributed to the development of the West — irrigation, power, reclamation — bears his mark, and the great Federal highway program which binds this country, together, which permits this State to be competitive east and west, north and south, this in large measure is his creation.

* Every character value is a sum of n m < sup > th </ sup > roots of unity, where n is the degree ( that is, the dimension of the associated vector space ) of the representation with character χ and m is the order of g. In particular, when F is the field of complex numbers, every such character value is an algebraic integer.

Every President of the United States from William Howard Taft to John F. Kennedy threw a ceremonial first pitch at least once at Griffith.

* " Every Time You Say I Love You " ( 1981 ) F & SF, May

Every sitting U. S. President since 1960 ( Eisenhower, John F. Kennedy, Lyndon B. Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, George H. W. Bush, Bill Clinton and George W. Bush ) has addressed a convention or attended an event at Cobo Center.

" Two Cars in Every Garage and Three Eyes on Every Fish " was the first episode produced for the second season, but " Bart Gets an F " aired first because of Bart's popularity and the producers wanted to premiere with an episode involving him in hopes of stealing viewers from The Cosby Show.

* Young, F. Every Man his own Mechanic ( 1881 )

* The New Dictionary of Cultural Literacy, Third Edition: What Every American Needs to Know Edited by James Trefil, Joseph F. Kett, and E. D. Hirsch.

" Every time I turn around, there's a new trial of the century ," says defense attorney F. Lee Bailey.

Every year since 1952, it has sponsored the Alfred Korzybski Memorial Lecture, with presenters from a broad range of disciplines, from science to medicine to entertainment, including names like actor Steve Allen, psychologist Albert Ellis, scientist and visionary R. Buckminster Fuller, linguist Allen Walker Read, and philosopher F. S. C. Northrop.

Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M.

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 year there is a volunteer of the year award and also the ' John D Hammer ' trophy for the ' Junior volunteer of the year '.

Every meromorphic function on D can be expressed as the ratio between two holomorphic functions ( with the denominator not constant 0 ) defined on D: any pole must coincide with a zero of the denominator.

Every year at the International Astronautical Congress, three prestigious awards are given out: the Allan D. Emil Memorial Award, the Franck J. Malina Astronautics Medal and the Luigi G. Napolitano Award.

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

The deputy director of the North Central Association of Colleges and Schools ( NCACS ), Steven D. Crow, says " Every move the university's made has been monitored " and MIU's library, faculty, academic mission and classroom space have been deemed appropriate.

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 element of D is the least upper bound of a countable increasing sequence of isolated elements.

Every domain D can be embedded in an ω-complete domain completion ( called the ω-completion or simply the completion of D ) that is, in a precise sense, the smallest ω-complete domain containing D. The isolated elements of completion are precisely the isolated elements of D, but in general completion contains limit points that are not found in D. completion is uniquely determined up to isomorphism.

* Why Does Nearly Every Culture Have a Tradition of a Global Flood John D. Morris, Ph. D.

Every member of the group has an alias by which he is known, the band's founding members adopting the personas Larry Love ( Rob Spragg ) and The Very Reverend Dr. D. Wayne Love ( Jake Black ).

* Every audience member had his or her own A / B / C / D keypad.

After gaining a minor role in Annie Hall in 1977, D ' Angelo appeared in a string of hit movies in the late 1970s, including Every Which Way But Loose, Hair, and Coal Miner's Daughter, the latter earning her a Golden Globe nomination for Best Supporting Actress and a Country Music Association award for Album of the Year.

Although the organization is secretive, it holds one regular public event each year, the National Prayer Breakfast held in Washington, D. C. Every sitting United States president since President Dwight D. Eisenhower, up to President Barack Obama, has participated in at least one National Prayer Breakfast during his term.

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

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

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.