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Polygraph (mathematics)
In mathematics, and particularly in category theory Category 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. Nowadays, cate ..., a polygraph is a generalisation of a directed graph. It is also known as a computad. They were introduced as "polygraphs" by Albert Burroni and as "computads" by Ross Street. In the same way that a directed multigraph can freely generate a category, an ''n''-computad is the "most general" structure which can generate a free n-category. References Category theory Directed graphs {{categorytheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cursive Writing
Cursive (also known as script, among other names) is any style of penmanship in which characters are written joined in a flowing manner, generally for the purpose of making writing faster, in contrast to block letters. It varies in functionality and modern-day usage across languages and regions; being used both publicly in artistic and formal documents as well as in private communication. Formal cursive is generally joined, but casual cursive is a combination of joins and pen lifts. The writing style can be further divided as "looped", " italic" or "connected". The cursive method is used with many alphabets due to infrequent pen lifting and beliefs that it increases writing speed. Despite this belief, more elaborate or ornamental styles of writing can be slower to reproduce. In some alphabets, many or all letters in a word are connected, sometimes making a word one single complex stroke. A study of gradeschool children in 2013 discovered that the speed of their cursive writing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Theory
Category 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. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the ''source'' and the ''target'' of the morphism. One often says that a morphism is an ''arrow'' that ''maps'' its source to its target. Morphisms can be ''composed'' if the target of the first morphism equals the source of the second one, and morphism compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Burroni
Albert may refer to: Companies * Albert (supermarket), a supermarket chain in the Czech Republic * Albert Heijn, a supermarket chain in the Netherlands * Albert Market, a street market in The Gambia * Albert Productions, a record label * Albert Computers, Inc., a computer manufacturer in the 1980s Entertainment * ''Albert'' (1985 film), a Czechoslovak film directed by František Vláčil * ''Albert'' (2015 film), a film by Karsten Kiilerich * ''Albert'' (2016 film), an American TV movie * ''Albert'' (Ed Hall album), 1988 * "Albert" (short story), by Leo Tolstoy * Albert (comics), a character in Marvel Comics * Albert (''Discworld''), a character in Terry Pratchett's ''Discworld'' series * Albert, a character in Dario Argento's 1977 film ''Suspiria'' Military * Battle of Albert (1914), a WWI battle at Albert, Somme, France * Battle of Albert (1916), a WWI battle at Albert, Somme, France * Battle of Albert (1918), a WWI battle at Albert, Somme, France People * Albe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ross Street
Ross Howard Street (born 29 September 1945, Sydney) is an Australian mathematician specialising in category theory.Street, Ross Howard (1945 - ) ''Biographical entry'', Encyclopaedia of Australian ScienceStreet, Ross Howard, FAA (1945-) trove.nla.gov.au Biography Street completed his undergraduate and postgraduate study at the , where his dissertation advisor was Max Kelly. He is a ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multigraph
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called ''parallel edges''), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge. There are two distinct notions of multiple edges: * ''Edges without own identity'': The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes. * ''Edges with own identity'': Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges. A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two. For some authors, the terms ''pseudograph'' and ''multigraph'' are synonymous. For others, a pseudograph is a multigraph that is permitted to have loops. Undirected multigraph (edges without ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Object
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set ''A'' can be thought of as being a "generic" algebraic structure over ''A'': the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure. Examples include free groups, tensor algebras, or free lattices. The concept is a part of universal algebra, in the sense that it relates to all types of algebraic structure (with finitary operations). It also has a formulation in terms of category theory, although this is in yet more abstract terms. Definition Free objects are the direct generalization to categories of the notion of basis in a vector space. A linear function between vector spaces is entirely determined by its values on a basis of the vector space The following definition translates this to any category. A concrete category is a category that is equipped with a faithf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category (mathematics)
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. A simple example is the category of sets, whose objects are sets and whose arrows are functions. '' Category theory'' is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Theory
Category 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. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the ''source'' and the ''target'' of the morphism. One often says that a morphism is an ''arrow'' that ''maps'' its source to its target. Morphisms can be ''composed'' if the target of the first morphism equals the source of the second one, and morphism compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
