Category (mathematics)In mathematics, a category (sometimes called an abstract category to distinguish it from a ) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the , whose objects are sets and whose arrows are functions. is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent.
Equivalence of categoriesIn , a branch of abstract mathematics, an equivalence of categories is a relation between two that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned.
Comma categoryIn mathematics, a comma category (a special case being a slice category) is a construction in . It provides another way of looking at morphisms: instead of simply relating objects of a to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere (Lawvere, 1963 p. 36), although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories. Comma categories also guarantee the existence of some s and colimits.
Empirical evidenceEmpirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms evidence and empirical are to be defined. Often different fields work with quite different conceptions.
Phase transitionIn chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.
Public companyA public company is a company whose ownership is organized via shares of stock which are intended to be freely traded on a stock exchange or in over-the-counter markets. A public (publicly traded) company can be listed on a stock exchange (listed company), which facilitates the trade of shares, or not (unlisted public company). In some jurisdictions, public companies over a certain size must be listed on an exchange. In most cases, public companies are private enterprises in the private sector, and "public" emphasizes their reporting and trading on the public markets.
Glass transitionThe glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased. An amorphous solid that exhibits a glass transition is called a glass. The reverse transition, achieved by supercooling a viscous liquid into the glass state, is called vitrification.
Energy policyEnergy policy is the manner in which a given entity (often governmental) has decided to address issues of energy development including energy conversion, distribution and use as well as reduction of greenhouse gas emissions in order to contribute to climate change mitigation. The attributes of energy policy may include legislation, international treaties, incentives to investment, guidelines for energy conservation, taxation and other public policy techniques. Energy is a core component of modern economies.
Higher category theoryIn mathematics, higher category theory is the part of at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants of spaces, such as their fundamental . An ordinary has and morphisms, which are called 1-morphisms in the context of higher category theory.
Critical infrastructureCritical infrastructure, or critical national infrastructure (CNI) in the UK, describes infrastructure considered essential by governments for the functioning of a society and economy and deserving of special protection for national security. Most commonly associated with the term are assets and facilities for: Shelter; Heating (e.g. natural gas, fuel oil, district heating); Agriculture, food production and distribution; Education, skills development and technology transfer / basic subsistence and unemployment rate statistics; Water supply (drinking water, waste water/sewage, stemming of surface water (e.
