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In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) 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.
Categories are distinct collections of concrete or abstract instances (category members) that are considered equivalent by the cognitive system. Using category knowledge requires one to access mental representations that define the core features of category members (cognitive psychologists refer to these category-specific mental representations as concepts).
Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the ...
For example, abstracting a ... Abstraction is one of Jung's 57 definitions in Chapter XI of Psychological Types. There is an abstract thinking, just as there is ...
Abstraction is the thought process in which ideas are distanced from objects. Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.
Abstract objects are most commonly used in philosophy, particularly metaphysics, and semantics. They are sometimes called abstracta in contrast to concreta. The term abstract object is said to have been coined by Willard Van Orman Quine. [5] Abstract object theory is a discipline that studies the nature and role of abstract objects. It holds ...
An example of this abstraction process is the generational development of programming language from the machine language to the assembly language and the high-level language. Each stage can be used as a stepping stone for the next stage. The language abstraction continues for example in scripting languages and domain-specific programming languages.
At the very least, category theoretic language clarifies what exactly these related areas have in common (in some abstract sense). Category theory has been applied in other fields as well, see applied category theory. For example, John Baez has shown a link between Feynman diagrams in physics and monoidal categories. [7]