* The free functor F: Set → Grp ( which assigns to every set S the free group over S ) is left adjoint to forgetful functor U and is, therefore, cocontinuous.

This way the free functor that builds the free object A from the set X becomes left adjoint to the forgetful functor.

The most general setting for a free object is in category theory, where one defines a functor, the free functor, that is the left adjoint to the forgetful functor.

The free functor F, when it exists, is the left adjoint to U. That is, takes sets X in Set to their corresponding free objects F ( X ) in the category C. The set X can be thought of as the set of " generators " of the free object F ( X ).

For the free functor to be a left adjoint, one must also have a Set-morphism.

Other types of forgetfulness also give rise to objects quite like free objects, in that they are left adjoint to a forgetful functor, not necessarily to sets.

Its left adjoint is a functor that sends quivers to the free category.

The above definition is based in set theory ; the category-theoretic definition generalizes this into a functor from the free quiver to the category of sets.

Then as we can take the free group functor.

It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the " most general " algebra containing V, in the sense of the corresponding universal property ( see below ).

Not until F. W. Winterbotham's book The Ultra Secret was published in 1974 did ex-Bletchley Park staff feel free to reveal something of their wartime work.

There can only be one copy of the F-plasmid in a given bacterium, either free or integrated, and bacteria that possess a copy are called F-positive or F-plus ( denoted F < sup >+</ sup >).

In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.

The free vector space F on V × W is defined by taking the vector space in which the elements of V × W are a basis.

The historically earlier Helmholtz free energy is defined as F = U − TS, where U is the internal energy, T is the absolute temperature, and S is the entropy.

In 1882, the German physicist and physiologist Hermann von Helmholtz coined the phrase ‘ free energy ’ for the expression E − TS, in which the change in F ( or G ) determines the amount of energy ‘ free ’ for work under the given conditions.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

Generally speaking, the F region has the highest concentration of free electrons and ions anywhere in the atmosphere.

In free space, H / m and F / m.

by Walter F. Tichy while he was at Purdue University as a free and more evolved alternative to the then-popular Source Code Control System ( SCCS ).

Judge Judith F. Hayes stated in her ruling, "... the Court finds the general purpose of the website to be a free speech forum wherein Defendant criticized the management of Plaintiff.

I. H. O. T. F. M .- Man is an ardent defender of Adam Smith's invisible hand metaphor, and usually intervenes in situations where the purity of free market economics is in jeopardy.

Informally, we can consider these products on the left hand side as being elements of the free group F =

Let S be a set and let F < sub > S </ sub > be the free group on S. Let R be a set of words on S, so R naturally gives a subset of F < sub > S </ sub >.

Writing in A. R. Orage's magazine The New Age, the poet and critic F. S. Flint ( a champion of free verse and modern French poetry ) was highly critical of the club and its publications.

Since 1938 the Chamber of Commerce has given free lemonade when the temperature has surpassed 90 ° F.

The chain complex for X is defined as follows: first find a free module F < sub > 1 </ sub > and a surjective homomorphism p < sub > 1 </ sub >: F < sub > 1 </ sub > → X.

Then one finds a free module F < sub > 2 </ sub > and a surjective homomorphism p < sub > 2 </ sub >: F < sub > 2 </ sub > → ker ( p < sub > 1 </ sub >).

Following the original roots of modern graffiti as a political force came another game title, Marc Eckō's Getting Up: Contents Under Pressure ( 2006 ), featuring a story line involving fighting against a corrupt city and its oppression of free speech, as in the Jet Set Radio series.

Set free, he supported his mother and three sisters by working in a Rotterdam shipyard, went to sea again at 19, briefly worked for the navy, but having rejoined the merchant fleet was captured once more in 1621 — this time by Barbary corsairs off Tunis.

Set in and around London, it depicts a power struggle between grown-up middle class people who are lucky to be free of real problems.

*" The Concept Of Love " by Hideki Naganuma ( as featured in both the Jet Set Radio Future and Ollie King original soundtracks ) contains a strong theme of free love, including a number of recurring sampled audio clips concerning the topic.

# Set: Marlene ’ s attempts to free Yuji from the laboratory in which he is being held are thwarted.

This leads to the next topic: free functors exist when C is a monad over Set.

Set eighteen-months after the series finale, the sisters are seen living happy demon free lives and have each entered into motherhood.

Set eighteen-months after the series finale, the sisters are seen living happy demon free lives and have each entered into motherhood.

Set eighteen-months after the series finale, the sisters are seen living happy demon free lives and have each entered into motherhood.

Set to become a restricted free agent in July 2006, the Avalanche chose to trade his negotiating rights to the Calgary Flames at the 2006 NHL Entry Draft in exchange for defenceman Jordan Leopold and two second round draft picks.

* The Heads Set ( Limited Edition ) ( 2010 ) – The box set was released exclusively in Greenwich Pizza outlets, and included a free box of pizza.

Set to become unrestricted free agents on July 1, 2009, Daniel and Henrik began negotiating with the Canucks in the off-season and were reported to have asked for 12-year, $ 63 million contracts in mid-June.

Set to become unrestricted free agents on 1 July 2009, Henrik and Daniel began negotiating with the Canucks in the off-season and were reported to have asked for 12-year, $ 63 million contracts in mid-June.

The forgetful functor U: Grp → Set have a left adjoint given by the composite KF: Set → Mon → Grp where F is the free functor.

Set during the height of the Cold War, The Shoes of the Fisherman opens as protagonist Kiril Pavlovich Lakota ( Anthony Quinn ), the Metropolitan Archbishop of Lviv, is unexpectedly set free after twenty years in a Siberian labor camp by his former jailer, Piotr Ilyich Kamenev ( Laurence Olivier ), now the premier of the Soviet Union.

* Lazy Eyes / Set me free Mar 1978 Mushroom K7070

Set free by the Teen Angels from his prehistoric block of glacier ice comes the world's first superhero, Captain Caveman!