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Movements, leaders, victories and the continuing fight for equality.
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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
Innovation, patents, science, technology and world-changing contributions.
Pioneers, champions, Negro Leagues, records, activism and excellence.
Meet the people whose lives, choices and achievements shaped the journey.
Black towns, communities, institutions and places where history happened.
Moments that changed communities, movements, institutions and the nation.
Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
| Founded | November 28, 2008 |
|---|---|
| Creator | Urs Schreiber |
| Website | ncatlab |
| Written in | Ruby, Python[1] |
The nLab is a wiki for research-level notes, expositions and collaborative work. It includes original research in mathematics, physics, and philosophy with a focus on methods from type theory, category theory, and homotopy theory. The nLab espouses the "n-point of view"[2] (a deliberate pun on Wikipedia's "neutral point of view"), which is that type theory, homotopy theory, category theory, and higher category theory provide a useful, unifying viewpoint for mathematics, physics and philosophy.
The n in n-point of view could refer to either n-categories as found in higher category theory, n-groupoids as found in both homotopy theory and higher category theory, or n-types as found in homotopy type theory.
The nLab was originally conceived to provide a repository for ideas (and even new research) generated in the comments on posts at the n-Category Café, a group blog run at the time by John C. Baez, David Corfield and Urs Schreiber. Eventually the nLab developed into an independent project, which has since grown to include whole research projects and encyclopedic material.[3]
Associated with the nLab is the nForum: an online discussion forum for announcement and discussion of nLab edits (the analog of Wikipedia's "talk" pages) as well as for general discussion of the topics covered in the nLab. The preferred way of contacting the nLab steering committee is to post on the nForum.[4] An experimental sub-project of the nLab is the 'Publications of the nLab', intended as a journal for refereed research articles that are published online and cross-hyperlinked with the main wiki. This sub-project appears to be inactive as of 2014.[5]
The nLab was set up on November 28, 2008 by Urs Schreiber using the Instiki software provided and maintained by Jacques Distler. Since May 2015 it runs on a server at Carnegie Mellon University that is funded in the context of Steve Awodey's Homotopy Type Theory MURI grant.[6] The domain ncatlab.org is owned by Urs Schreiber.
The nLab is listed on MathOverflow as a standard online mathematics reference to check before asking questions.[7] Many questions and answers link to the nLab for background material.[8] It is one of two wikis mentioned by the mathematical physicist John C. Baez in his review of math blogs for the American Mathematical Society.[9]
There is an informal steering committee, which does not run the nLab,[4] but exists in order to resolve issues that could cause the whole project to run into trouble.
The content of this wiki is not placed under a specific copyright license.[10]
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
The nLab is a wiki for research-level notes, expositions and collaborative work. It includes original research in mathematics, physics, and philosophy with a focus on methods from type theory, category theory, and homotopy theory. The nLab espouses the "n-point of view" (a deliberate pun on Wikipedia's "neutral point of view"), which is that type theory, homotopy theory, category theory, and higher category theory provide a useful, unifying viewpoint for mathematics, physics and philosophy. The n in n-point of view could refer to either n-categories as found in higher category theory, n-groupoids as found in both homotopy theory and higher category theory, or n-types as found in homotopy type theory.
In mathematics and computer science, an event structure describes sequences of events that can be triggered by combinations of other events, with certain forbidden combinations of events. Different sources provide more or less flexible mathematical formalizations of how events can be triggered and which combinations are forbidden. Glynn Winskel gave the most general of these formalizations. Winskel formalizes an event structure as a triple ( E , C , ⊢ ) {\displaystyle (E,{\mathcal {C}},\vdash )} , in which: E {\displaystyle E} is a set of events, not necessarily finite. C {\displaystyle {\mathcal {C}}} is a family of finite subsets of E {\displaystyle E} , the subsets that are deemed to be consistent (not forbidden). If C ∈ C {\displaystyle C\in {\mathcal {C}}} is one of these consistent sets, then every subset of C {\displaystyle C} must also be consistent. That is, C {\displaystyle {\mathcal {C}}} must be closed under the operation of taking subsets. ⊢ {\displaystyle \vdash } is a binary relation from consistent sets to elements of E {\displaystyle E} . The relation C ⊢ e {\displaystyle C\vdash e} , for C ∈ C {\displaystyle C\in {\mathcal {C}}} and e ∈ E {\displaystyle e\in E} is interpreted as meaning that when the events so far form set C {\displaystyle C} , this enables e {\displaystyle e} to be the next event. When C ⊢ e {\displaystyle C\vdash e} , it is required that C ′ ⊢ e {\displaystyle C'\vdash e} for every consistent superset C ′ {\displaystyle C'} (with C ⊂ C ′ {\displaystyle C\subset C'} and C ′ ∈ C {\displaystyle C'\in {\mathcal {C}}} ). According to Winskel's definitions, a configuration of an event structure is a subset of E {\displaystyle E} all of whose finite subsets are consistent and whose events are all secured. Here, an event is secured when it belongs to a finite sequence of events from the configuration, each of which is enabled by the subset of earlier events from the same sequence. The nlab simplifies these definitions in two ways: It replaces the family of consistent events by an irreflexive symmetric relation # {\displaystyle \#} called incompatibility (or conflict), such that a finite set of events is consistent if and only if it contains no incompatible pair. And (either separately or with both simplifications together) it replaces the enabling relation by a partial order relation on E {\displaystyle E} called causal dependency, such that each event has finitely many predecessors, all of which must have happened earlier to enable the event. For the event structures with both simplifications, which nlab calls prime event structures, the configurations are the downward-closed subsets of the partial order that include no incompatible pairs.
In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), 𝒫(S), P(S), P ( S ) {\displaystyle \mathbb {P} (S)} , or 2S. Any subset of P(S) is called a family of sets over S.
Paul Adrien Maurice Dirac ( dih-RAK; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for both quantum electrodynamics and quantum field theory, coining the former term. He was Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969, and a professor of physics at Florida State University from 1970 to 1984. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." Dirac graduated from the University of Bristol with a Bachelor of Science in Electrical Engineering in 1921, and a Bachelor of Arts in Mathematics in 1923. Dirac then graduated from St John's College, Cambridge, with a Doctor of Philosophy in Physics in 1926, writing the first ever thesis on quantum mechanics. Dirac formulated the Dirac equation, one of the most important results in physics, in 1928. The equation connected special relativity and quantum mechanics and predicted the existence of antimatter. The equation has been regarded by some physicists as "the real seed of modern physics". Dirac wrote a famous paper in 1931, which further predicted the existence of antimatter. Dirac also contributed greatly to the reconciliation of general relativity with quantum mechanics. He contributed to Fermi–Dirac statistics, which describes the behaviour of fermions, particles with half-integer spin. His 1930 monograph, The Principles of Quantum Mechanics, is one of the most influential texts on the subject. In 1987, Abdus Salam declared that "Dirac was undoubtedly one of the greatest physicists of this or any century ... No man except Einstein has had such a decisive influence, in so short a time, on the course of physics in this century." In 1995, Stephen Hawking stated that "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe." Antonino Zichichi asserted that Dirac had a greater impact on modern physics than Einstein while Stanley Deser remarked that "We all stand on Dirac's shoulders."
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →The Greenwood District.
