A category C consists of the following three mathematical entities:

A ( covariant ) functor F from a category C to a category D, written, consists of:

A category intuitively consists of a collection of objects, and defined relationships between them.

Since plug-ins and extensions both increase the utility of the original application, Mozilla uses the term " add-on " as an inclusive category of augmentation modules that consists of plug-ins, themes, and search engines.

Grand theft generally consists of the theft of something of value over $ 1000 ( it can be money, labor or property but is lower with respect to various specified property ), while petty theft is the default category for all other thefts.

An initial morphism from X to U is an initial object in the category of morphisms from X to U. In other words, it consists of a pair ( A, φ ) where A is an object of D and φ: X → U ( A ) is a morphism in C, such that the following initial property is satisfied:

If ( E, M ) is a factorization system, then the morphisms in M may be regarded as the embeddings, especially when the category is well powered with respect to M. Concrete theories often have a factorization system in which M consists of the embeddings in the previous sense.

A category C consists of

The category Rel consists of all sets, with binary relations as morphisms.

In this sense, each monoid is a category that consists of one object and a collection of specific morphisms to itself.

Then an enriched category C ( alternatively, in situations where the choice of monoidal category needs to be explicit, a category enriched over M, or M-category ), consists of

The predrum category consists of simple drum-like percussion instruments.

A concrete category, when defined without reference to the notion of a category, consists of a class of objects, each equipped with an underlying set ; and for any two objects A and B a set of functions, called morphisms, from the underlying set of A to the underlying set of B.

In the study of comparative religion, the category of Abrahamic religions consists of the three monotheistic religions, Christianity, Islam and Judaism, which claim Abraham ( Hebrew Avraham א ַ ב ְ ר ָ ה ָ ם ; Arabic Ibrahim إبراهيم ) as a part of their sacred history.

Let F and G be two sheaves on X with values in the category C. A morphism φ: G → F consists of a morphism φ ( U ): G ( U ) → F ( U ) for each open set U of X, subject to the condition that this morphism is compatible with restrictions.

The ecrs module identifier consists of either chk, sks, ksk or loc followed by a slash and a category specific value.

Since plug-ins and extensions both increase the utility of the original application, Mozilla uses the term " add-on " as an inclusive category of augmentation modules that consists of plug-ins, themes, and search engines.

* The center of a monoidal category C consists of pairs ( A, u ) where A is an object of C, and a natural isomorphism satisfying certain axioms.

If is a category, a monad on consists of a functor together with two natural transformations: ( where denotes the identity functor on ) and ( where is the functor from to ).

The Jew's harp, jaw harp, mouth harp, Ozark harp, trump or juice harp, is a lamellophone instrument, which is in the category of plucked idiophones: it consists of a flexible metal or bamboo tongue or reed attached to a frame.

When we look at countries like Iran, Iraq, Pakistan, and Burma, where substantial progress has been made in creating a minimum supply of modern men and of social overhead capital, and where institutions of centralized government exist, we find a second category of countries with a different set of problems and hence different priorities for policy.

Shout at Eichmann though he might, the Prosecutor could not establish that the defendant was falsifying the way he felt about Jews or that what he did feel fell into the generally recognized category of anti-Semitism.

Alexander Grothendieck's work during the ` Golden Age ' period at IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis.

The film also won the Critics ' Award at Fantasporto, and was nominated for the International Fantasy Film Award in the category of Best Film in 1993.

To address this growing practice, and to restore integrity to the game, at its December 1868 meeting the NABBP established a professional category for the 1869 season.

A separate " award " was soon enacted for Night BASE jumping when Mayfield completed each category at night, becoming Night BASE # 1, with Smith qualifying a few weeks later.

This duality, which is transparent at the level of category theory, is often obscured in applications and can lead to surprising relationships.

Work under the supervision of the Team Leader, providing START triage for victims found at the scene ; marking victims with category of injury per the standard operating procedures ; when not accomplishing their primary mission, assist the Fire Suppression Team if needed, assist the Search and Rescue Team if needed, assist in the Medical Triage Area if needed, assist in the Treatment Area if needed, other duties as assigned ; communicate with Team Leader.

Furthermore, in 2011 Academic Ranking of World Universities ( ARWU ) rankings, TU / e was placed at the 52-75 bucket internationally in Engineering / Technology and Computer Science ( ENG ) category and at 34th place internationally in the Computer Science subject field.

Diagonal functor: The diagonal functor is defined as the functor from D to the functor category D < sup > C </ sup > which sends each object in D to the constant functor at that object.

A permission can either be a hunting license, gun ownership license (" Waffenbesitzkarte ", for sporting, collecting and self-defense at home or work ) or a carry permit (" Waffenpass ", for carrying a loaded weapon outside of the owner's home or workplace ), with the ownership license being the most common way to category B gun ownership.

As with category C, every Austrian citizen at the age of 18 or over can buy and own this type of weapon without further registration or permission, since no background checks are performed also EU / EEA citizens can buy them without problems.

The much more numerous category of vici, " small towns " grew on informal plans, often round a camp or at a ford or crossroads ; some were not small, others were scarcely urban, some not even defended by a wall, the characteristic feature of a place of any importance.

The Japfa Classic in Denpasar, Bali, Indonesia, was a category XVI event of 10 players in which included Alexander Khalifman – at the time FIDE world champion – and Anatoly Karpov – his predecessor.

Donburi, a combo of an entrée on a big bowl of rice, is another familiar category of dishes, but in Japan these are standard fare served at the shokudō or " Japanese style cafeteria / cheap restaurant ".

Brabham soon " seemed to merge into Cooper Cars ": he was not an employee, but he started working at Cooper on a daily basis from the midpoint of the 1955 season building a Bobtail mid-engined sports car, intended for Formula One, the top category of single seater racing.

" For her work, she won the Best Actress Silver Ombú category award at the 2002 Mar del Plata Film Festival.

On April 23, 2012 at Internet Society's Global INET conference in Geneva, Switzerland, Torvalds was one of the inaugural inductees into the Internet Hall of Fame, one of ten in the Innovators category and thirty-three overall inductees.

The 2008 – 09 Manchester display, titled " Lindow Man: A Bog Body Mystery Exhibition at the Manchester Museum ", won the category " Best Archaeological Innovation " in the 2010 British Archaeological Awards, run by the Council for British Archaeology.

Mustelids are diverse and the largest family in the order Carnivora, at least partly because in the past it has been a catch-all category for many early or poorly differentiated taxa.

In a study of individuals diagnosed with " severe mental illness " living in a US inner-city area, a quarter were found to have been victims of at least one violent crime over the course of a year, a proportion eleven times higher than the inner-city average, and higher in every category of crime including violent assaults and theft.

Foodservice establishments of this category did not accept any different customers on walk-in basis, but instead, only accepted customers who came as a group and ordered banquets by appointment, and the banquets provided by foodservice establishments of this category often included most, if not all tables, at the site.

The bulk of the business of foodservice of this category, however, was catering at the topnotch customers ’ homes or other locations, and such catering was often for birthdays, marriages, funerals, promotions and other important celebrations / festivals.