Additionally, these could either be " Interferral " or " Non-Interferral ".

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

A systematic study of category theory then allows us to prove general results about any of these types of mathematical structures from the axioms of a category.

V-chip is a generic term for technology used in television set receivers in the USA, Canada, and Brazil which allows the blocking of programs based on their ratings category.

It allows the embedding of any category into a category of functors ( contravariant set-valued functors ) defined on that category.

Stacking allows graphical representations of how many albums there are in a specific category or folder.

This " vertical composition " of natural transformation is associative and has an identity, and allows one to consider the collection of all functors itself as a category ( see below under Functor categories ).

This allows to define new local structures on the category ( such as a closure operator ).

* In the category of interpretations of an algebraic model, the initial object is the initial algebra, the interpretation that provides as many distinct objects as the model allows and no more.

Some schools have an intermediate category, passing at the master's level, which allows the student to leave with a master's without having completed a master's thesis.

Finding a generator of an abelian category allows one to express every object as a quotient of a direct sum of copies of the generator.

The category of covering morphisms of a groupoid G is also equivalent to the category of actions of G on sets, and this allows the recovery of more traditional classifications of coverings.

Hillcrest Labs won the " Best Of Innovations " award in the video accessories category for software and hardware that allows a television to be controlled with natural gestures.

Some schools have an intermediate category, passing at the master's level, which allows the student to leave with a master's without having completed a master's thesis.

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

This then allows a category theory approach: what remains to do is to re-express the gluing conditions.

The groupoid also allows for groupoids a notion of homotopy: it is a unitinterval object in the category of groupoids.

The Big Rock Eddies has evolved year after year, celebrating its 17th anniversary in 2010 — now including a Student category that allows post secondary students to compete with their peers for prize money.

The testing was completed at more than 25 Level I trauma centers in the United States under a Food and Drug Administration special category ( 21CFR 50. 24 ) in 1996 that allows its use without patient consent in special circumstances.

This category allows “ for situations in which there is little, if any, market activity for the asset or liability at the measurement date .” FASB explains that “ observable inputs ” are gathered from sources other than the reporting company and that they are expected to reflect assumptions made by market participants. In contrast, “ unobservable inputs ” are not based on independent sources but on “ the reporting entity ’ s own assumptions about the assumptions market participants would use .” The entity may only rely on internal information if the cost and effort to obtain external information is too high.

Since 2000, the Census Bureau allows individuals to identify more than one racial / ethnic category on the census form, although it does not yet have a multiracial category.

William Smythe, director of field service, told the commissioners that Multnomah, as of Aug. 22, had spent $58,918 out of its budgeted $66,000 in the category, leaving only $7,082 for the rest of the month.

** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.

His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory into its foundations.

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.

Homological algebra is category theory in its aspect of organising and suggesting manipulations in abstract algebra.

Basic constructions, such as the fundamental group or fundamental groupoid of a topological space, can be expressed as fundamental functors to the category of groupoids in this way, and the concept is pervasive in algebra and its applications.

If one statement is true in a category C then its dual will be true in the dual category C < sup > op </ sup >.

The United States Environmental Protection Agency ( EPA ) includes discarded CRT monitors in its category of " hazardous household waste " but considers CRTs that have been set aside for testing to be commodities if they are not discarded, speculatively accumulated, or left unprotected from weather and other damage.

* A scientific field ( a branch of science ) – widely-recognized category of specialized expertise within science, and typically embodies its own terminology and nomenclature.

Power hour and its variant, centurion, fall under this category.

In a 6 optional meet, the divers will yet again perform one dive from each category, but this time they will perform a 6th optional from the category of their choosing, which is worth its actual DD from the DD sheet.

In 2006, The Princeton Review ranked Dartmouth third in its " Quality of Life " category, and sixth for having the " Happiest Students.

When they claim that their product is the " best ", they mean that the product is as good as the other superior products in its category.

A key aim was to base categorization on colloquial English descriptive language ( which would be easier to use by federal administrative offices ), rather than assumptions of etiology, although its categorical approach assumed each particular pattern of symptoms in a category reflected a particular underlying pathology ( an approach described as " neo-Kraepelinian ").

The calendar also shows the costs of the next city improvement in each of the three categories — as a city is improved in a category, that segment has its card flipped down calendar style to reveal the newly built improvement, any advantages gained by the improvement, and the updated cost of upgrading to the next level in that category.

Since history and memory ( representations of or belief about the past ) are distinct in all philosophy and ontology from plan, vision or intent ( representations of or will to change the future ), statements that confuse these are category errors: No statement about history or memory can imply a similar statement about a plan or vision or intent, nor vice versa-a distinction sometimes credited to Hume who distinguished also the morality of a statement from its truth.

In this context the term " professional " ( used for the first category ) as opposed to " amateur " ( used for the second and third ) refers only to the professionalism of the used medium, and not to the professionalism of the language itself or its creator.

Limit functor: For a fixed index category J, if every functor J → C has a limit ( for instance if C is complete ), then the limit functor C < sup > J </ sup >→ C assigns to each functor its limit.

Dual vector space: The map which assigns to every vector space its dual space and to every linear map its dual or transpose is a contravariant functor from the category of all vector spaces over a fixed field to itself.

Tangent and cotangent bundles: The map which sends every differentiable manifold to its tangent bundle and every smooth map to its derivative is a covariant functor from the category of differentiable manifolds to the category of vector bundles.