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Page "Epimorphism" ¶ 5
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Every and morphism
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 morphism f: G → H in Grp has a category-theoretic kernel ( given by the ordinary kernel of algebra ker f =

Every and concrete
* Every wall, both interior and exterior of the Avengers Tower is made of a vibranium reinforced concrete.
Every usage of an array or struct type instantiates a new concrete type, or reuses a previous instantiated type.
Every year, MEDEF International organises a number of delegations of French business leaders with concrete projects to targeted countries, especially developing countries.
OKI has been working to achieve a better global environment for the next generation and has built the system of “ Company-wide network-type environmental management .” Every year OKI creates an environmental protection activity program, " OKI Eco Plan 21 " to reduce environmental impacts continuously and to promote concrete efforts for the targets set in the program.
The Commission on the Status of Women ( CSW or UNCSW ) is a functional commission of the United Nations Economic and Social Council ( ECOSOC ), one of the main UN organs within the United Nations. Every year, representatives of Member States gather at United Nations Headquarters in New York to evaluate progress on gender equality, identify challenges, set global standards and formulate concrete policies to promote gender equality and advancement of women worldwide.
But his religion in developed form, as we find it, in his Navavidhan, is full of concrete symbols of all religions .... Every Hindu is conscious of the underlying unity of this universalism.

Every and category
* 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 epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.
Every pre-abelian category is of course an additive category, and many basic properties of these categories are described under that subject.
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 and whose
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 root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
# Every sequence in A has a convergent subsequence, whose limit lies in A.
Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.
Every cycle climaxes in the arrival of The Leveler, whose approach ( and fall ) is heralded by an ominous comet that appears in the sky.
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes ( or congruence classes ) for the relation.
* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.
Every family head in the Mafia selects a man whose characteristics already make him look approachable.
* Every root of a monic polynomial whose coefficients are algebraic integers is itself an algebraic integer.
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 ).
She was raised there by her mother, Ellen Simmons, whose Sioux name was Taté Iyòhiwin ( Every Wind or Reaches for the Wind ).
* Every Parliament constituted in conformity with the laws of a sovereign State whose population it represents and on whose territory it functions may request affiliation to the Inter-Parliamentary Union.
" A man's home is his castle " is translated in Gor as, " Every man is an Ubar within the circle of his sword " ( The Ubar is a war-leader, a General who takes power at a time of crisis, and whose rule is tantamount to tyrant until the crisis is resolved.
* Every planar graph whose faces all have even length is bipartite.
During this period he lived with the French poet Pierre Martory, whose books Every Question but One ( 1990 ), The Landscape Is behind the door ( 1994 ) and The Landscapist he has translated ( 2008 ), as he has Jean Perrault ( Camouflage ), Max Jacob ( The Dice Cup ), Pierre Reverdy and Raymond Roussel.
Every governor since Ronald Reagan in 1968 has been subject to a recall effort, but Gray Davis was the first governor whose opponents gathered the necessary signatures to qualify for a special election.
Every artist she showed the script to had declined to take on the project, so it was offered to aspiring artist Arthur Adams, whose samples had been given to editor Carl Potts and Nocenti, his assistant editor, by editor Al Milgrom.
* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.
* Every constant function whose domain and codomain are the same is idempotent.
* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to

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