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

Added 3 weeks ago by Zeta

42

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

Added month ago by Zeta

59

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

Added 2 months ago by Zeta

45

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

Added 2 months ago by sandra

171

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

Added 2 months ago by sandra

164

from pebble to pebble - sea, oceans, rocks, coasts
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from pebble to pebble

Added 2 months ago by sandra

135

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

Added 2 months ago by sandra

94

Landscape - colorful jigsaw puzzle
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Landscape

Added 2 months ago by andi

68

Lighthouse - colorful jigsaw puzzle
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Lighthouse

Added 3 months ago by andi

230

Landscape - colorful jigsaw puzzle
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Landscape

Added 4 months ago by andi

135

landscape - colorful puzzle landscapes
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landscape

Added 4 months ago by natalia

101

Landscape - colorful jigsaw puzzle
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Landscape

Added 4 months ago by andi

194

Landscape - colorful jigsaw puzzle
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Landscape

Added year ago by andi

330

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

377

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

138

LIBANLIBAN - LIBANLIBANLIBANLIBAN
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LIBANLIBAN

Added year ago by LIBAN

102

Wyspy Kanaryjskie - widok na Ocean Spokojny
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Wyspy Kanaryjskie

Added year ago by Julia

216

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

Added year ago by polinne

558

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

Added over a year ago by Irena

364

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

Added over a year ago by wieslawa

129

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

Added over a year ago by wieslawa

328 1

Niecodzienne cuda natury - Niecodzienne cuda natury
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Niecodzienne cuda natury

Added over a year ago by Anita

86

Niecodzienne cuda natury - Niecodzienne cuda natury
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Niecodzienne cuda natury

Added over a year ago by Anita

165

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

Added over a year ago by wieslawa

173

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

Added over a year ago by Anabell

587 1

niesamowity widok - co stworzyła woda z ziemi
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niesamowity widok

Added over a year ago by Basieńka

245

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

210

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

141

nad oceanem - piękna plaża w Portugalii
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nad oceanem

Added over a year ago by Fifka

450

Zielona Irlandia - Klify u wybrzeży Irlandii
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Zielona Irlandia

Added over a year ago by Majeczka

398

Skalista wyspa - Skały i lazurowe morze a niebem tworzą naturalną  całość.
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Skalista wyspa

Added over a year ago by Julka

111

Duża skała - Duża skała stojąca pośrodku morza.
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Duża skała

Added over a year ago by Karolina

153

The-Guardian-Adraga - Landschaft The-Guardian-Adraga
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The-Guardian-Adraga

Added over a year ago by Balduin

215

Durchblick-II - Klippenwanderung von der Praia Marinha Richtung Porches
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Durchblick-II

Added over a year ago by Balduin

165