Information: - In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms. - Category theory formalizes mathematical structure and its concepts in terms of a collection of "objects" and of "arrows" (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. - In the mathematical theory of categories , a sketch is a category D , together with a set of limit cones and a set of colimit cones . A model of the sketch in a category C is a functor M : D \ rightarrow C that takes each specified cone to a limit cone in C and each specified cocone to a colimit cocone in C. Morphisms of models are natural transformations . Sketches are a general way of specifying structures on the objects of a category , forming a category - theoretic analog to the logical concept of a theory and its models . They allow multisorted models and models in any category . Sketches were invented in 1968 by Charles Ehresmann , using a different but equivalent definition . There are still other definitions in the research literature . - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word "homomorphism" comes from the ancient Greek language: " (homos)" meaning "same" and " (morphe)" meaning "form" or "shape". - In mathematics, a functor is a type of mapping between categories arising in category theory. Functors can be thought of as homomorphisms between categories. In the category of small categories, functors can be thought of more generally as morphisms. After reading the paragraphs above, we are interested in knowing the entity with which 'sketch ' exhibits the relationship of 'facet of'. Find the answer from the choices below. Choices: - algebra - category theory - mathematics
category theory

Information: - Distant Waves is a novel using the RMS Titanic as much of its setting . It is not a story completely of the Titanic , it mixes fiction with real people that were alive during the Titanic era . - Harland & Wolff Heavy Industries is an Northern Irish heavy industrial company, specialising in shipbuilding and offshore construction, located in Belfast, Northern Ireland. Harland & Wolff is most famous for having built all of the ships intended for the White Star Line including . Other well known ships built by Harland & Wolff include "Titanic"s sister ships and RMS "Britannic", the Royal Navy's , Royal Mail Line's "Andes", Shaw Savill's , Union-Castle's , and P&O's . Harland and Wolff's official history, "Shipbuilders to the World", was published in 1986. - Belfast is the capital and largest city of Northern Ireland, the second largest on the island of Ireland, and the heart of the tenth largest Primary Urban Area in the United Kingdom. On the River Lagan, it had a population of 286,000 at the 2011 census and 333,871 after the 2015 council reform. Belfast was granted city status in 1888. - RMS "Titanic" was a British passenger liner that sank in the North Atlantic Ocean in the early morning of 15April 1912, after colliding with an iceberg during her maiden voyage from Southampton to New York City. Of the 2,224 passengers and crew aboard, more than 1,500 died, making it one of the deadliest commercial peacetime maritime disasters in modern history. The largest ship afloat at the time it entered service, the RMS "Titanic" was the second of three "Olympic" class ocean liners operated by the White Star Line, and was built by the Harland and Wolff shipyard in Belfast. Thomas Andrews, her architect, died in the disaster. - The City of New York, often called New York City or simply New York, is the most populous city in the United States. With an estimated 2015 population of 8,550,405 distributed over a land area of just , New York City is also the most densely populated major city in the United States. Located at the southern tip of the state of New York, the city is the center of the New York metropolitan area, one of the most populous urban agglomerations in the world. A global power city, New York City exerts a significant impact upon commerce, finance, media, art, fashion, research, technology, education, and entertainment, its fast pace defining the term "New York minute". Home to the headquarters of the United Nations, New York is an important center for international diplomacy and has been described as the cultural and financial capital of the world. - The Oceanic Steam Navigation Company or White Star Line of Boston Packers, more commonly known as just White Star Line, was a prominent British shipping company. Founded in 1845, the line operated a fleet of clipper ships that sailed between Britain and Australia. Today it is most famous for their innovative vessel "Oceanic" of 1870, and the Olympic class ocean liners, including the ill-fated RMS "Titanic". After reading the paragraphs above, we are interested in knowing the entity with which 'distant waves' exhibits the relationship of 'operator'. Find the answer from the choices below. Choices: - ireland - royal mail - southern - united kingdom - white star line
white star line