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Algebraic geometry category satisfying lifting conditions
In algebraic geometry, a prestack F over a category C equipped with some Grothendieck topology is a category together with a functor p: F → C satisfying
Prestack
Topological space
X,i=1,...,m} . There is an analog of a Ran space for a scheme: the Ran prestack of a quasi-projective scheme X over a field k, denoted by Ran ( X ) {\displaystyle
Ran_space
the following are the most important: anisotropic parameter estimation, prestack depth anisotropy migration, and fracture characterization based on anisotropy
Seismic_anisotropy
type; i.e., they simply forget extra data. See also: fibred category, prestack. The dual of a cartesian fibration is called an op-fibration; in particular
Cartesian_fibration
Mathematical mapping between objects arising from their definitions
of canonical maps or canonical isomorphisms; for a typical example, see prestack. If N is a normal subgroup of a group G, then there is a canonical surjective
Canonical_map
Technique from algebraic geometry
the language of stacks, flat descent is exactly the statement that the prestack of quasi-coherent sheaves is a stack with respect to étale (or fpqc) topology
Faithfully_flat_descent
Algebraic geometry analog of a principal bundle in algebraic topology
base forms a stack. Conversely, a prestack can be stackified by taking the category of torsors (over the prestack). If G {\displaystyle G} is a connected
Torsor_(algebraic_geometry)
Generalisation of a sheaf; a fibered category that admits effective descent
stacks, rather than of prestacks. The category c is called a stack over the category C with a Grothendieck topology if it is a prestack over C and every descent
Stack_(mathematics)
Category mapping
pseudofunctor, which is a category-valued presheaf, is often also called a prestack (a stack minus effective descent). A pseudofunctor F from a category C
Pseudo-functor
of groupoids. This way, each groupoid object determines a prestack in groupoids. This prestack is not a stack but it can be stackified to yield a stack
Groupoid_object
Trough off the coast of Japan
doi:1029/2005/B003835. Pisani, P., Reshef, M., Moore, G., 2005, Targeted 3-D prestack depth imaging at Legs 190-196 ODP drill sites (Nankai Trough, Japan), Geophysical
Nankai_Trough
Turkish geophysicist
industry, he earned his PhD from Stanford in 1979. His dissertation on prestack partial migration was a major contribution to seismic processing. Yılmaz
Öz_Yılmaz
Reflection seismology consortium (1973-)
seismic applications such as velocity estimation, wavefield-continuation prestack migration, multidimensional image estimation, and 4-D (time-lapse) reservoir
Stanford Earth imaging Project
Stanford_Earth_imaging_Project
Type of functor
q\circ f=p} . More generally, one can also consider a morphism between prestacks (a stackification would be an example). One particular important example
Morphism_of_algebraic_stacks
Concept in differential geometry
presentation or cover of the stack X {\displaystyle X} . Recall that a prestack (of groupoids) on a category C {\displaystyle {\mathcal {C}}} , also known
Differentiable_stack
Concept in algebraic geometry
functor. Via p, Vect n {\displaystyle \operatorname {Vect} _{n}} is a prestack over C. That it is a stack over C is precisely the statement "vector bundles
Moduli stack of vector bundles
Moduli_stack_of_vector_bundles
stacks. Hopf algebroid - encodes the data of quasi-coherent sheaves on a prestack presentable as a groupoid internal to affine schemes (or projective schemes
Sheaf_on_an_algebraic_stack
Generalization of a category
presheaf is commonly called a prestack. Thus, C ^ {\displaystyle {\widehat {C}}} can be thought of consisting of ∞-prestacks. (With a choice of a functor
Quasi-category
Concept in mathematics
equation. If X is a scheme (or more generally, stack, derived stack, or even prestack), we can associate to it its so-called de Rham stack, denoted XdR. This
Connection_(principal_bundle)
sense, this is the ultimate answer to the problem. Roughly, a "quotient prestack" is the category of orbits and one stackify (i.e., the introduction of
Group-scheme_action
Standard that diagrams must satisfy up to isomorphism
achieved by choosing canonical isomorphisms. But in some cases, such as prestacks, there can be several canonical isomorphisms and there might not be an
Coherency_(homotopy_theory)
cartesian morphisms. cartesian morphism 1. Given a functor π: C → D (e.g., a prestack over schemes), a morphism f: x → y in C is π-cartesian if, for each object
Glossary_of_category_theory
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Boy/Male
Arabic Muslim
One who serves a kind man.
Boy/Male
Indian
Honor, Respect
Boy/Male
English American French
Fortified. See also Berlyn.
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Power and Dignity of Indra
Boy/Male
Hindu
Conqueror of the ocean
Boy/Male
Latin
Great.
Boy/Male
Arabic, Australian, French, Hebrew, Muslim
Oldest Son
Boy/Male
English
Area of Birch Trees
Girl/Female
Hindu, Indian
Angle
Boy/Male
British, English
Golden Friend
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