representability การใช้

• This generalizes the representability of ordinary cohomology by Eilenberg MacLane spaces.
• Other important representability results are related to the cardinality of the semilattice.
• It is weaker in the sense that it does not of itself imply representability.
• A version of the representability theorem in the case of Grothendieck duality theorem in algebraic geometry.
• One of the advantages of one-dimensional persistence is its representability by a diagram or barcode.
• He included in his paper a single theorem which is a necessary condition of the representability of matroids.
• One basic result is that the representable functors on the homotopy category have a simple characterisation ( the Brown representability theorem ).
• Note that this representability requirement relies on the first constraint ( Domain of f should be equal to domain of s ).
• Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids.
• Although some authors include reflexivity as one of the axioms required to obtain representability ( this axiom states that A \ ! \ succsim \!
• Brown also proved a general categorical version of the representability theorem, which includes both the version for pointed connected CW complexes and the version for spectra.
• The abstract conditions being known for this ( Brown's representability theorem ) ensure that the result, as an existence theorem, is affirmative and not too difficult.
• Jacob Lurie has proved a version of the Brown representability theorem for the homotopy category of a pointed quasicategory with a compact set of generators which are cogroup objects in the homotopy category.
• Since the pioneer efforts of Frisch in the 1920s, one of the major issues which has pervaded the theory of preferences is the representability of a preference structure with a real-valued function.
• In mathematics, "'Brauer's theorem "', named for Richard Brauer, is a result on the representability of 0 by forms over certain fields in sufficiently many variables.
• In 1955 Patrick Suppes and Muriel Winet solved the issue of the representability of preferences by a cardinal utility function, and derived the set of axioms and primitive characteristics required for this utility index to work.
• Sheaves can be furthermore generalized to stacks in the sense of Grothendieck, usually with some additional representability conditions leading to Artin stacks and, even finer, Deligne-Mumford stacks, both often called algebraic stacks.
• Under appropriate hypotheses ( e . g ., flat, proper, finitely presented ), any morphism T \ to S of algebraic spaces yields a restriction of scalars functor that takes algebraic stacks to algebraic stacks, preserving properties such as Artin, Deligne-Mumford, and representability.
• The matroids of branchwidth three are not well-quasi-ordered without the additional assumption of representability over a finite field, but nevertheless the matroids with any finite bound on their branchwidth have finitely many minimal forbidden minors, all of which have a number of elements that is at most exponential in the branchwidth.
• A second construction, due to Jacob Lurie, constructs tmf rather by describing the moduli problem it represents and applying general representability theory to then show existence : just as the moduli stack of elliptic curves represents the functor that assigns to a ring the category of elliptic curves over it, the stack together with the sheaf of E-infinity ring spectra represents the functor that assigns to an E-infinity ring its category of oriented derived elliptic curves, appropriately interpreted.