Category theoryCategory theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory is used in almost all areas of mathematics. In particular, numerous constructions of new mathematical objects from previous ones that appear similarly in several contexts are conveniently expressed and unified in terms of categories.
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.
Atmosphere of JupiterThe atmosphere of Jupiter is the largest planetary atmosphere in the Solar System. It is mostly made of molecular hydrogen and helium in roughly solar proportions; other chemical compounds are present only in small amounts and include methane, ammonia, hydrogen sulfide, and water. Although water is thought to reside deep in the atmosphere, its directly measured concentration is very low. The nitrogen, sulfur, and noble gas abundances in Jupiter's atmosphere exceed solar values by a factor of about three.
ThoughtIn their most common sense, the terms thought and thinking refer to conscious cognitive processes that can happen independently of sensory stimulation. Their most paradigmatic forms are judging, reasoning, concept formation, problem solving, and deliberation. But other mental processes, like considering an idea, memory, or imagination, are also often included. These processes can happen internally independent of the sensory organs, unlike perception.
Current densityIn electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Assume that A (SI unit: m2) is a small surface centred at a given point M and orthogonal to the motion of the charges at M.
Strict 2-categoryIn , a strict 2-category is a with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category. It can be formally defined as a category over Cat (the , with the structure given by ). The concept of 2-category was first introduced by Charles Ehresmann in his work on enriched categories in 1965. The more general concept of (or weak 2-category), where composition of morphisms is associative only up to a 2-isomorphism, was introduced in 1968 by Jean Bénabou.
Analytical psychologyAnalytical psychology (Analytische Psychologie, sometimes translated as analytic psychology and referred to as Jungian analysis) is a term coined by Carl Jung, a Swiss psychiatrist, to describe research into his new "empirical science" of the psyche. It was designed to distinguish it from Freud's psychoanalytic theories as their seven-year collaboration on psychoanalysis was drawing to an end between 1912 and 1913. The evolution of his science is contained in his monumental opus, the Collected Works, written over sixty years of his lifetime.
Intrusive thoughtAn intrusive thought is an unwelcome, involuntary thought, image, or unpleasant idea that may become an obsession, is upsetting or distressing, and can feel difficult to manage or eliminate. When such thoughts are associated with obsessive-compulsive disorder (OCD), Tourettes syndrome (TS), depression, body dysmorphic disorder (BDD), and sometimes attention-deficit hyperactivity disorder (ADHD), the thoughts may become paralyzing, anxiety-provoking, or persistent.
Analytic philosophyAnalytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods, prominent in Europe. Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G.
Analytical mechanicsIn theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics.
Analytical MarxismAnalytical Marxism is an academic school of Marxist theory which emerged in the late 1970s, largely prompted by G. A. Cohen's Karl Marx's Theory of History: A Defence (1978). In this book, Cohen drew on the Anglo–American tradition of analytic philosophy in an attempt to raise the standards of clarity and rigor within Marxist theory, which led to his distancing of Marxism from continental European philosophy. Analytical Marxism rejects much of the Hegelian and dialectical tradition associated with Marx's thought.
Quantum field theoryIn theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.
