* Every small category has a skeleton.

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

* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

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 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 epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.

Every morphism in a concrete category whose underlying function is surjective is an epimorphism.

Every person born into this world comes from one of these categories in order to help fulfill the kind of function that that category of people is supposed to fulfill in order to keep the community together.

* Every non-empty Baire space is of second category in itself, and every intersection of countably many dense open subsets of X is non-empty, but the converse of neither of these is true, as is shown by the topological disjoint sum of the rationals and the unit interval 1.

Every monoidal category is monoidally equivalent to a strict monoidal category.

Every group G can be viewed as a category with a single object ( morphisms in this category are just the elements of G ).

Every ring can be viewed as a preadditive category with a single object.

Every year a set of students are selected from each sports category for ' Inter IIT Sports Meet ', a set of sporting events occur in the winter at any one of the IIT's.

Every object in a Grothendieck category has an injective hull.

Every NNO is an initial object of the category of diagrams of the form

Every category has a host of untranslatable jokes that rely on linguistic puns, wordplay, and Russian's vocabulary of foul language.

Every U. S. and foreign charity that qualifies as tax-exempt under Section 501 ( c )( 3 ) of the Internal Revenue Code is considered a " private foundation " unless it demonstrates to the IRS that it falls into another category.

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

Every abelian category is an exact category if we just use the standard interpretation of " exact ".

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

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 dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

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 lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every field is, of course, one-dimensional over its center.

Every fifteen minutes they played a record ; the rest of the time it was commercials about a high-school correspondence course.

Every state now, of course, has a Board of Pharmacy which regulates the practice of pharmacy.

Every summer the town holds a jazz festival with local pubs, clubs, hotels and various other venues playing host to live jazz music over the course of a weekend.

( Every object is, of course, an improper part of itself.

Every summer since 1997, an English teacher has offered a one-week summer course in writing and photography.

Every student is also required to take an introductory news reporting course called J200, ( named after its course designation.

Chekhov wrote The Cherry Orchard during the course of several years, alternating between periods of lighthearted giddiness and despondent frustration which he considered as bordering upon sloth ( in a letter he wrote, " Every sentence I write strikes me as good for nothing.

" Every generation in Israel carries within itself the remnants of worlds created and destroyed during the course of the previous history of the Jewish people.

Every subject or course successfully completed earns ‘ credits ’ towards the SACE.

Every student enrolled in a course at Thompson Rivers University is a member of the Students ' Union.

The 2008 feature-length documentary " Every Little Step " chronicles the casting process of A Chorus Line's 2006 revival, with re-created choreography by Bennett's long-time associate Baayork Lee, and, in the course of the film, the saga of the original production is re-told as well, through the use of old film clips and revealing interviews from the original collaborators, including Lee, Bob Avian ( who was the show's original co-choreographer with Bennett and the director of the revival ), composer Marvin Hamlisch and the original's leading lady, Donna McKechnie.

Every week between two and twelve plays ( determined by two rolls of a die by someone in the audience ) are removed from the " menu " and replaced with new plays, written in the course of the week.

Every year of every course should have at least one course rep.

Every year, the college admits 200 students to the undergraduate ( MBBS ) course.

Every year the fight ends in a draw, and as the masters are getting old, they decide the best course of action is to each take on a student to determine who is the better teacher.

" Every year, the river changes its course and branches anew, for which reason it is sometimes called the " Branch River.

for the purpose of sale or of building development: Every division of a piece of land into two or more lots, parcels or parts is, of course, a subdivision.

Every effort is made to enable the preferred choice of course requested by students to be timetabled but where an option is not viable in terms of numbers and / or staffing, the Governors reserve the right to withdraw the subject option offer.

These landmarks have different properties that help the environment in some way, improving unpopular spots and otherwise calming down angry golfers ( Every part of the course is rated in this way, so that players have to raise its value with fun, skill and intelligence to have customers like it ).

Every year 150 students are admitted to the MBBS course based on the rank in the West Bengal Joint Entrance Examination ( WBJEE ) and also through All India Pre Medical Test ( AIPMT ) conducted by the Central Board of Secondary Education.

Every stage had a winning cyclist ( the cyclist who crossed the finish line first, or in case of a time trial who took the shortest time to complete the course ) and a team that wins the daily team classification ( the team of which the three best cyclists had the lowest accumulated time ).