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William Lawvere
Francis William Lawvere (; born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics. Biography Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory while teaching a course on functional analysis for Truesdell, specifically from a problem in John L. Kelley's textbook ''General Topology''. Lawvere found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. Truesdell supported Lawvere's application to study further with Samuel Eilenberg, a founder of category theory, at Columbia University in 1960. Before completing the Ph.D. Lawvere spent a year in Berkeley as an informal student of model theory and set theory, following lectures by Alfred Tarski and Dana Scott. In his first teaching position at Reed College he was instructed to devise courses in calculus and abstract algebra from a foundational persp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Muncie, Indiana
Muncie ( ) is an incorporated city and the county seat, seat of Delaware County, Indiana, Delaware County, Indiana. Previously known as Buckongahelas Town, named after the legendary Delaware Chief.http://www.delawarecountyhistory.org/history/docs/lenape-villages.pdf It is located in East Central Indiana, about northeast of Indianapolis. The 2020 United States Census, United States Census for 2020 reported the city's population was 65,194. It is the principal city of the Muncie metropolitan statistical area, which has a population of 117,671. The Lenape (Delaware (tribe), Delaware) people, led by Buckongahelas arrived in the area in the 1790s, founding several villages, including one known as Munsee Town, along the White River (Indiana), White River. The trading post, renamed Muncietown, was selected as the Delaware County seat and platted in 1827. Its name was officially shortened to Muncie in 1845 and incorporated as a city in 1865. Muncie developed as a manufacturing and indus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjoint Functors
In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of "optimal solutions" to certain problems (i.e., constructions of objects having a certain universal property), such as the construction of a free group on a set in algebra, or the construction of the Stone–Čech compactification of a topological space in topology. By definition, an adjunction between categories \mathcal and \mathcal is a pair of functors (assumed to be covariant) :F: \mathcal \rightarrow \mathcal and G: \mathcal \rightarrow \mathcal and, for all objects X in \mathcal and Y in \mathcal a bijection between the respective morphism s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifiers (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has the property P. Othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Logic
__NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970. Overview There are three important themes in the categorical approach to logic: ;Categorical semantics: Categorical logic introduces the notion of ''structure valued in a category'' C with the classical model theoretic notion of a structure appearing in the particular case where C is the category of sets and functions. This notion has proven useful when the set-theoretic notion of a model lacks generality and/or is inconvenient. R.A.G. Seely's modeling of va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alex Heller
Alex is a given name. It can refer to a shortened version of Alexander, Alexandra, Alexis. People Multiple *Alex Brown (other), multiple people * Alex Gordon (other), multiple people *Alex Harris (other), multiple people *Alex Jones (other), multiple people * Alexander Johnson (other), multiple people *Alex Taylor (other), multiple people Politicians *Alex Allan (born 1951), British diplomat *Alex Attwood (born 1959), Northern Irish politician *Alex Kushnir (born 1978), Israeli politician *Alex Salmond (born 1954), Scottish politician, former First Minister of Scotland Baseball players *Alex Avila (born 1987), American baseball player * Alex Bregman (born 1994), American baseball player *Alex Gardner (baseball) (1861–1921), Canadian baseball player *Alex Katz (baseball) (born 1994), American baseball player *Alex Pompez (1890–1974), American executive in Negro league baseball and Major League Baseball scout *Alex Rodrigu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville.. He was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space. He was the oldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor at Rice University and Purdue University. Another sister died as a baby. His father and grandfather were both ministers; his grandfather had been a Presbyterian, but was kicked out of the church for believing in evolution, and his father was a Congregationalist. His mother, Winifred, studied at Mount Holyoke College and taught English, Latin, and mathematics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oberwolfach
Oberwolfach ( gsw, label= Low Alemannic, Obberwolfä) is a town in the district of Ortenau in Baden-Württemberg, Germany. It is the site of the Oberwolfach Research Institute for Mathematics, or Mathematisches Forschungsinstitut Oberwolfach. Geography Geographical situation The town of Oberwolfach lies between 270 and 948 meters above sea level in the central Schwarzwald (Black Forest) on the river Wolf, a tributary of the Kinzig. Neighbouring localities The district is neighboured by Bad Peterstal-Griesbach to the north, Bad Rippoldsau-Schapbach in Landkreis Freudenstadt to the east, by the towns of Wolfach and Hausach to the south, and by Oberharmersbach Oberharmersbach ( gsw, label= Low Alemannic, Haamerschbach) is a town in the district of Ortenau in Baden-Württemberg in Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second ... to the west. References External links Gemeinde Oberwolfach: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Gabriel
Pierre Gabriel (1 August 1933 – 24 November 2015), also known as Peter Gabriel, was a French mathematician at the University of Strasbourg (1962–1970), University of Bonn (1970–1974) and University of Zürich (1974–1998) who worked on category theory, algebraic groups, and representation theory of algebras. He was elected a correspondent member of the French Academy of Sciences in November 1986. His most famous result is Gabriel's theorem that provides a classification of all quiver (mathematics), quivers of finite type. References External links * * Personal Web Page 1933 births 2015 deaths 20th-century French mathematicians 21st-century French mathematicians Algebraists University of Paris alumni University of Zurich faculty Members of the French Academy of Sciences People from Bitche French expatriates in Germany French expatriates in Switzerland {{Mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Theory
Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Sentential logic is the subset of first-order logic involving only algebraic sentences. The notion is very close to the notion of algebraic structure, which, arguably, may be just a synonym. Saying that a theory is algebraic is a stronger condition than saying it is elementary. Informal interpretation An algebraic theory consists of a collection of ''n''-ary functional terms with additional rules (axioms). For example, the theory of groups is an algebraic theory because it has three functional terms: a binary operation ''a'' × ''b'', a nullary operation 1 (neutral element), and a unary operation ''x'' ↦ ''x''−1 with the rules of associativity, neutrality and inverses respectively. Other examples include: * the theory of semigroups * the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reed College
Reed College is a private liberal arts college in Portland, Oregon. Founded in 1908, Reed is a residential college with a campus in the Eastmoreland neighborhood, with Tudor-Gothic style architecture, and a forested canyon nature preserve at its center. Referred to as one of "the most intellectual colleges in the country", Reed is known for its mandatory first-year humanities program, senior thesis, progressive politics, de-emphasis on grades, academic rigor, grade deflation, and unusually high proportion of graduates who go on to earn doctorates and other postgraduate degrees. The college has many prominent alumni, including over a hundred Fulbright Scholars, 67 Watson Fellows, and three Churchill Scholars; its 32 Rhodes Scholars are the second-highest count for a liberal arts college. Reed is ranked fourth in the United States for all postsecondary institutions for the percentage of its graduates who go on to earn a Ph.D., after Caltech, Harvey Mudd, and Swarthmore Colleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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