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stack

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations of situations where isomorphic, compatible geometrical objects (such as vector bundles on topological spaces) can be "glued together" within a restriction of the topological basis. In a more general set-up the restrictions are replaced with pullbacks; fibred categories then make a good framework to discuss the possibility of such gluing. The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topology. Thus a stack is formally given as a fibred category over another base category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology.
A beach. - A beach - I do not know where.
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A beach.

Added 3 weeks ago by Mila

43

Cliffs in Australia. - Cliffs Twelve Apostles in Australia.
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Cliffs in Australia.

Added month ago by Zeta

41

Landscape - colorful jigsaw puzzle
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Landscape

Added month ago by andi

47

BAJKOWY VIEW - Vacation, holidays, rest.
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BAJKOWY VIEW

Added 2 months ago by ada

25

BAJKOWY VIEW - Vacation, holidays, rest.
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BAJKOWY VIEW

Added 2 months ago by ada

52

The coast of England. - The coast of England. Cliffs in Dorset.
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The coast of England.

Added 3 months ago by Zeta

49

Cliff in Normandy. - Sea cliff in Normandy.
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Cliff in Normandy.

Added 3 months ago by Zeta

71

Coast in Scotland. - Coast in Scotland in the UK.
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Coast in Scotland.

Added 4 months ago by Zeta

55

wonders of nature - sea ​​landscape, coast, ocean,
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wonders of nature

Added year ago by sandra

183

seaside landscape - sea, ocean, coast, cliffs
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seaside landscape

Added year ago by sandra

177

hole rock - sea, ocean, rocks, coast
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hole rock

Added year ago by sandra

98

Landscape - colorful jigsaw puzzle
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Landscape

Added year ago by andi

70

Lighthouse - colorful jigsaw puzzle
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Lighthouse

Added year ago by andi

242

Landscape - colorful jigsaw puzzle
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Landscape

Added year ago by andi

138

landscape - colorful puzzle landscapes
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landscape

Added year ago by natalia

104

Landscape - colorful jigsaw puzzle
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Landscape

Added year ago by andi

199

Landscape - colorful jigsaw puzzle
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Landscape

Added year ago by andi

340

Azure Window - no longer existing rock bridge off the coast of the island of Gozo in the Republic of Malta
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Azure Window

Added year ago by Z&S

378

Azure Window - A non-existent rock bridge off the coast of the island of Gozo in the Republic of Malta.
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Azure Window

Added year ago by Z&S

77

IRELAND - IRELAND
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IRELAND

Added year ago by IRLANDIA

140

LIBANLIBAN - LIBANLIBANLIBANLIBAN
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LIBANLIBAN

Added year ago by LIBAN

106

Wyspy Kanaryjskie - widok na Ocean Spokojny
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Wyspy Kanaryjskie

Added year ago by Julia

218

Cypr po prostu - wakacje, morze, ciepło
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Cypr po prostu

Added over a year ago by polinne

563

Italia, Capri, Faraglioni - pojedyncze skaly w płd-zach cześci Capri
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Italia, Capri, Faraglioni

Added over a year ago by Irena

378

skała jak zwierzę - skała,słoń,woda,zieleń
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skała jak zwierzę

Added over a year ago by wieslawa

130

błękitne groty - Grecja,skały groty,woda,zieleń
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błękitne groty

Added over a year ago by wieslawa

331 1

Niecodzienne cuda natury - Niecodzienne cuda natury
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Niecodzienne cuda natury

Added over a year ago by Anita

87

Niecodzienne cuda natury - Niecodzienne cuda natury
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Niecodzienne cuda natury

Added over a year ago by Anita

168

Gargano Włochy - skały,drzewa,morze,kształty
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Gargano Włochy

Added over a year ago by wieslawa

175

Hiszpańskie wybrzeże... - Hiszpańskie wybrzeże a zachodzie słońca
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Hiszpańskie wybrzeże...

Added over a year ago by Anabell

591 1

niesamowity widok - co stworzyła woda z ziemi
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niesamowity widok

Added over a year ago by Basieńka

248

Hiszpańskie wybrzeże - Hiszpańskie wybrzeże
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Hiszpańskie wybrzeże

Added over a year ago by Anabell

770

Italia - Wyspa Capri - Italia - Capri. Przy południowo-wschodniej części wyspy spotkać można najbardziej charakterysty
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Italia - Wyspa Capri

Added over a year ago by Anabell

213

Italia - Wyspa Capri - Italia - Capri. Przy południowo-wschodniej części wyspy spotkać można najbardziej charakterysty
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Italia - Wyspa Capri

Added over a year ago by Anabell

145

nad oceanem - piękna plaża w Portugalii
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nad oceanem

Added over a year ago by Fifka

453