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Triangulated categories admit a notion of cohomology, and every triangulated category has a large supply of cohomological functors. A cohomological functor F from a triangulated category D to an abelian category A is a functor such that for every exact triangle [],
The first formula are relevant to multiplication algorithm#Quarter square multiplication. In 1796, Gauss discovered that every positive integer is representable as a sum of three triangular numbers, writing in his diary his famous words, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ". The three triangular numbers are not necessarily distinct, or nonzero ...
A DG category C is called pre-triangulated if it has a suspension functor and a class of distinguished triangles compatible with the suspension, such that its homotopy category Ho(C) is a triangulated category. A triangulated category T is said to have a dg enhancement C if C is a pretriangulated dg category whose homotopy category is ...
In the branch of mathematics called homological algebra, a t-structure is a way to axiomatize the properties of an abelian subcategory of a derived category.A t-structure on consists of two subcategories (,) of a triangulated category or stable infinity category which abstract the idea of complexes whose cohomology vanishes in positive, respectively negative, degrees.
3. In computer science, denotes the (unknown) greatest lower bound for the exponent of the computational complexity of matrix multiplication. 4. Written as a function of another function, it is used for comparing the asymptotic growth of two functions. See Big O notation § Related asymptotic notations. 5.
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Triangulated category
arcosech – inverse hyperbolic cosecant function. (Also written as arcsch.) arcosh – inverse hyperbolic cosine function. arcoth – inverse hyperbolic cotangent function. arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.) arcsec – inverse secant function. arcsin – inverse sine function. arctan – inverse ...
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...