Virtual Topology and Functor Geometry
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A01=Fred Van Oystaeyen
aA FiB
Abelian Category
abstract algebra structures
Adjoint Functors
advanced mathematical physics
Author_Fred Van Oystaeyen
category
category theory applications
Category=PBF
Category=PBM
Category=PBW
Category=PHU
Covariant Functor
dynamical topology in noncommutative spaces
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Exact Functor
Exact Sequence
finitely
Finitely Generated Objects
Full And Faithful Functors
Functorial Morphisms
generated
graded
Graded Rings
grothendieck
Grothendieck Categories
Grothendieck Topology
Hereditary Torsion Theories
Kernel Functors
Left Exact
Left Exact Preradicals
noncommutative geometry
Observed Truth
ore
Ore Set
quantum gravity mathematics
Quantum Points
quotient
Quotient Category
Quotient Objects
sets
Sheaf Theory
sheafification methods
theory
torsion
Torsion Class
Torsion Free Class
Torsion Theory
Product details
- ISBN 9781138430297
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 27 Jul 2017
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra.
Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory.
By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.
