In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy...

Representability in mathematics can refer to the existence of a representable functor in category theory Birch's theorem about the representability of...

universal bundle) along a map X → B G {\displaystyle X\to BG} . Brown's representability theorem guarantees the existence of classifying spaces. The idea that...

Smash product Adjunction space Cohomotopy Cohomotopy group Brown's representability theorem Eilenberg–MacLane space Fibre bundle Möbius strip Line bundle...

mathematics including: Brown's representability theorem Brown–Peterson cohomology Brown–Gitler spectrum His publications include: Brown, Edgar H. Jr. (1959)...

contravariant functor from C to Set. Brown's representability theorem in algebraic topology says that this functor is represented by a CW-complex K(Z,n) called...

Browder–Minty theorem (operator theory) Brown's representability theorem (homotopy theory) Bruck–Chowla–Ryser theorem (combinatorics) Brun's theorem (number...

object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This...

homotopy category of CW complexes, existence theorems for universal bundles arise from Brown's representability theorem. We will first prove: Proposition. Let...

conditions being known for this (Brown's representability theorem) ensure that the result, as an existence theorem, is affirmative and not too difficult...

{\displaystyle K(\mathbb {Z} ,2)} . Because of this fact, and Brown's representability theorem, we have the following isomorphism H 2 ( X ; Z ) ≅ [ X , C...

Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called Van Kampen's theorem, expresses the...

spectrum S 0 {\displaystyle S^{0}} . Amnon Neeman generalized the Brown representability theorem to any compactly generated triangulated category, as follows...

result is that the representable functors on the homotopy category have a simple characterisation (the Brown representability theorem). Abstract cell complex...

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with...

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as a sum of four non-negative integer...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

commonly written as ln(x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among...

is Brauer's theorem on induced characters. In mathematics, Brauer's theorem, named for Richard Brauer, is a result on the representability of 0 by forms...

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...

The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges....

find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number...

In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable...

Classifying space, for the case n = 1 {\displaystyle n=1} Brown representability theorem, regarding representation spaces Moore space, the homology analogue...

In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose...

2020-08-19. Brown 1991, Definition III.2.1 Brown 1991, Theorem III.2.12 Brown 1991, Corollary III.2.16 Mirsky 1990, Theorem 1.4.1 Brown 1991, Theorem III.3...

mathematics, Belyi's theorem on algebraic curves states that any non-singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann...

impossibility theorem is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social...

Brown 1991, Definition III.2.1 Brown 1991, Theorem III.2.12 Brown 1991, Corollary III.2.16 Mirsky 1990, Theorem 1.4.1 Brown 1991, Theorem III.3.18 Eigen means "own"...