Nerve (category theory)In , a discipline within mathematics, the nerve N(C) of a C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory. The nerve of a category is often used to construct topological versions of moduli spaces.
Group isomorphismIn abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
Wi-FiWi-Fi (ˈwaɪfaɪ) is a family of wireless network protocols based on the IEEE 802.11 family of standards, which are commonly used for local area networking of devices and Internet access, allowing nearby digital devices to exchange data by radio waves. These are the most widely used computer networks in the world, used globally in home and small office networks to link devices together and to a wireless router to connect them to the Internet, and in wireless access points in public places like coffee shops, hotels, libraries, and airports to provide visitors with Internet connectivity for their mobile devices.
CarA car, or an automobile is a motor vehicle with wheels. Most definitions of cars say that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people, not cargo. French inventor Nicolas-Joseph Cugnot built the first steam-powered road vehicle in 1769, while French-born-Swiss inventor François Isaac de Rivaz designed and constructed the first internal combustion powered automobile in 1808. The modern car—a practical, marketable automobile for everyday use—was invented in 1886, when German inventor Carl Benz patented his Benz Patent-Motorwagen.
Li-FiLi-Fi (also written as LiFi) is a wireless communication technology which utilizes light to transmit data and position between devices. The term was first introduced by Harald Haas during a 2011 TEDGlobal talk in Edinburgh. Li-Fi is a light communication system that is capable of transmitting data at high speeds over the visible light, ultraviolet, and infrared spectrums. In its present state, only LED lamps can be used for the transmission of data in visible light.
CommutingCommuting is periodically recurring travel between one's place of residence and place of work or study, where the traveler, referred to as a commuter, leaves the boundary of their home community. By extension, it can sometimes be any regular or often repeated travel between locations, even when not work-related. The modes of travel, time taken and distance traveled in commuting varies widely across the globe. Most people in least-developed countries continue to walk to work.
Effects of the car on societiesSince the start of the twentieth century, the role of cars has become highly important, though controversial. They are used throughout the world and have become the most popular mode of transport in many of the more developed countries. In developing countries, the effects of the car on society are not as visible, however they are nonetheless significant. The development of the car built upon the transport sector first started by railways. This has introduced sweeping changes in employment patterns, social interactions, infrastructure and the distribution of goods.
SuffixIn linguistics, a suffix is an affix which is placed after the stem of a word. Common examples are case endings, which indicate the grammatical case of nouns and adjectives, and verb endings, which form the conjugation of verbs. Suffixes can carry grammatical information (inflectional endings) or lexical information (derivational/lexical suffixes). Inflection changes the grammatical properties of a word within its . Derivational suffixes fall into two categories: class-changing derivation and class-maintaining derivation.
Category of small categoriesIn mathematics, specifically in , the category of small categories, denoted by Cat, is the whose objects are all and whose morphisms are functors between categories. Cat may actually be regarded as a with natural transformations serving as 2-morphisms. The initial object of Cat is the empty category 0, which is the category of no objects and no morphisms. The terminal object is the terminal category or trivial category 1 with a single object and morphism. The category Cat is itself a , and therefore not an object of itself.
Natural capitalNatural capital is the world's stock of natural resources, which includes geology, soils, air, water and all living organisms. Some natural capital assets provide people with free goods and services, often called ecosystem services. All of these underpin our economy and society, and thus make human life possible. It is an extension of the economic notion of capital (resources which enable the production of more resources) to goods and services provided by the natural environment.
CarpoolCarpooling is the sharing of car journeys so that more than one person travels in a car, and prevents the need for others to have to drive to a location themselves. By having more people using one vehicle, carpooling reduces each person's travel costs such as: fuel costs, tolls, and the stress of driving. Carpooling is also a more environmentally friendly and sustainable way to travel as sharing journeys reduces air pollution, carbon emissions, traffic congestion on the roads, and the need for parking spaces.
Russian grammarRussian grammar employs an Indo-European inflexional structure, with considerable adaptation. Russian has a highly inflectional morphology, particularly in nominals (nouns, pronouns, adjectives and numerals). Russian literary syntax is a combination of a Church Slavonic heritage, a variety of loaned and adopted constructs, and a standardized vernacular foundation. The spoken language has been influenced by the literary one, with some additional characteristic forms.
