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...

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...

the following are the most important: anisotropic parameter estimation, prestack depth anisotropy migration, and fracture characterization based on anisotropy...

of canonical maps or canonical isomorphisms; for a typical example, see prestack. For a discussion of the problem of defining a canonical map see Kevin...

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...

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...

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...

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...

seismic applications such as velocity estimation, wavefield-continuation prestack migration, multidimensional image estimation, and 4-D (time-lapse) reservoir...

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...

presheaf is commonly called a prestack. Thus, C ^ {\displaystyle {\widehat {C}}} can be thought of consisting of ∞-prestacks. (With a choice of a functor...

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...

industry, he earned his PhD from Stanford in 1979. His dissertation on prestack partial migration was a major contribution to seismic processing. Yılmaz...

q\circ f=p} . More generally, one can also consider a morphism between prestacks (a stackification would be an example). One particular important example...

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...

stacks. Hopf algebroid - encodes the data of quasi-coherent sheaves on a prestack presentable as a groupoid internal to affine schemes (or projective schemes...

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...

presentation or cover of the stack X {\displaystyle X} . Recall that a prestack (of groupoids) on a category C {\displaystyle {\mathcal {C}}} , also known...

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...

achieved by choosing canonical isomorphisms. But in some cases, such as prestacks, there can be several canonical isomorphisms and there might not be an...

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...

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...