The Yoneda lemma suggests that instead of studying the ( locally small ) category C, one should study the category of all functors of C into Set ( the category of sets with functions as morphisms ).

If C is a locally small category ( i. e. the hom-sets are actual sets and not proper classes ), then each object A of C gives rise to a natural functor to Set called a hom-functor.

Set into the pavement of Fore Street is the ' Brutus Stone ', a small granite boulder onto which, according to local legend, Brutus first stepped from his ship.

* The forgetful functor U: Grp → Set creates ( and preserves ) all small limits and filtered colimits ; however, U does not preserve coproducts.

" Set in a small town in Alabama in 1900, it focuses on the struggle for control of the family business.

Set in a small town in north Texas during the year November 1951 – October 1952, it is about the coming of age of Sonny Crawford ( Timothy Bottoms ) and his friend Duane Jackson ( Jeff Bridges ).

# If C is any small category, then there exists a faithful functor P: Set < sup > C < sup > op </ sup ></ sup > → Set which maps a presheaf X to the coproduct.

Set against the economic boom from oil revenue it became apparent that the Land Reforms did not make life better for the rural population: according to Amid, ".. only a small group of rural people experienced increasing improvements in their welfare and poverty remained the lot of the majority ".

The two Exeter undergraduates, together with a small group of Jones ' friends from Birmingham known as the Birmingham Set, speedily formed a very close and intimate society, which they called " The Brotherhood ".

# A more technologically sophisticated system uses Set Meters, which are small devices connected to televisions in selected homes.

* If C is a small category, then the functor category Set < sup > C </ sup > consisting of all covariant functors from C into the category of sets, with natural transformations as morphisms, is cartesian closed.

Set in the early 1960s among the Irish Catholic community in a small Yorkshire town, the book is about a 30 year-old mummy's boy and his attempts at liberating himself from his domineering mother.

Digital Leisure worked with a small independent game developer, Derek Sweet, to release a CD-ROM 4-Disc Box Set for Windows based PCs.

Set in a non-descript period, it retains many of the elements of the original tale, although twists the story by changing the main protagonist from a boy to a small girl, as well as altering the ending so that is the mother instead who finds herself punished.

Landing quays sit near three small hamlets known as Set Bunder in the north-west, Mora Bunder in the northeast, and Gharapuri or Raj Bunder in the south.

* if C is any small category, then the category Set < sup > C </ sup > of presheaves is a topos.

* Set, a small tuber or bulb used instead of seed, especially:

Set in Toronto during the early 1980s, it follows the CEO of a small cable station who stumbles upon a broadcast signal featuring extreme violence and torture.

Set in the New York City borough of The Bronx, the show starred Ted Danson as John Becker, a misanthropic doctor who operates a small practice and is constantly annoyed by his patients, co-workers, friends, and practically everything and everybody else in his world.

Set back behind the parapet is an attic with small windows that forms a lantern above the entrance hall.

Let C be a locally small category and let Set be the category of sets.

Set in an unnamed African country after independence, the book is narrated by Salim, an ethnically Indian Muslim and a shopkeeper in a small, growing city in the country's remote interior.

Set in a fictional German town named Lebensbaum ( Life's Tree ), Shadow of Memories revolves around a 22-year-old man named Eike Kusch, who dies in the beginning of the game from being stabbed after leaving a small diner.

Set apart from the glowing underside, the darker, nonluminescent collar tapers at both sides of the throat, and has been hypothesized to serve as a lure by mimicking the silhouette of a small fish from below.

Set in the White Mountains, large portions of the town are within the White Mountain National Forest.

Perhaps most intriguing in terms of the pre-Dynasty XX connections between temples of Set and nearby temples of his consort Nephthys is the evidence of Papyrus Bologna, which preserves a most irritable complaint lodged by one Pra ' em-hab, Prophet of the " House of Seth " in the now-lost town of Punodjem (" The Sweet Place ").

Set in the coastal town of Brighton, England, Dirty Weekend follows the story of Bella, a mild-mannered secretary who works from home in a basement flat.

The Papyrus Bologna records a complaint lodged by a prophet of the temple of Set in that town regarding undue taxation in his regard.

Set in Venetian Slovenia, the novel, published under a pseudonym in the Yugoslav town of Ljubljana, described the efforts of a local Roman Catholic priest to preserve the use of Slovene language in church against the policies of the Italian Fascist regime.

Set among the Berkshire Mountains, Stockbridge is drained by the Housatonic River, which runs through the center of town.

The town is also mentioned in the 1974 country song "( We're Not ) The Jet Set ," in which George Jones and Tammy Wynette sing about road tripping around the Midwestern and Southern part of the United States in a Chevrolet while falling in love.

Set astride the broad Israel River valley, the town commands remarkable views of the Presidential Range and other White Mountain summits.

Set in the White Mountains, the town is surrounded by the White Mountain National Forest.

Set into the pavement, outside the museum, is an ornate example of Coade stone work, in the form of ammonites, reflecting both local history ( Eleanor Coade ) and the palaeontology for which the town is famous.

Set in a fictional Midlands town, the series followed the romantic and professional lives of its doctors and nurses.

Set in a nondescript American town, Ghost World follows the misadventures of two best friends, Enid ( Thora Birch ) and Rebecca ( Scarlett Johansson ) who detest their high school classmates and delight in mocking others.

Set in 1935 in the town of Harley-on-the-Hudson, a drifter named Henry Stauf, after murdering a woman, had dreams of beautiful dolls which he would then carve and give to the local children.

Set in 1960s Yorkshire, in the fictional town of Ashfordly and the nearby village of Aidensfield in the North Riding of Yorkshire, the motorcycle-riding Aidensfield village bobby was originally played by Nick Berry.

Set primarily in the United States and particularly in Malibu, California, an excitingly exotic locale to romantic girls trapped in a sleepy Welsh town, the stories concerned young men and women who become involved in strange and often criminal behaviour.

Set in the fictional town of Corinth, Pennsylvania, the early years of the show revolved around the blue-collar Donovans and the blue-blood Aldens.

Set in 1917, it followed the efforts of a film crew to make a silent melodrama in a resort town while the Revolution rages around them.

About a mile south of the river and the ghost town of Pahreah is the Paria Movie Set which was the site for a number of western movies.

Set in the town of Griffin Rock, Maine, a group of Autobots – Heatwave, Boulder, Blades and Chase – respond to Optimus Prime's message for any active Autobots to arrive to Earth.

Set in the rural town of Hooterville, the show followed the goings-on at The Shady Rest Hotel, of which Kate Bradley ( Bea Benaderet ) was the proprietor.

Set in the fictional town of Los Barcos on the Costa del Sol in Spain and based around the lives of British and European expats, the BBC hoped it would be as successful as EastEnders and replicate some of the sunshine and glamour of imported Australian soaps such as Home and Away and Neighbours.

Set in the early 1930s, the film takes up the story of Grace ( Bryce Dallas Howard ) and her father ( Willem Dafoe ) after burning the town of Dogville at the end of the previous film.