Stalk (sheaf)The stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open sets, but the underlying topological space consists of points. It is reasonable to attempt to isolate the behavior of a sheaf at a single fixed point of . Conceptually speaking, we do this by looking at small neighborhoods of the point. If we look at a sufficiently small neighborhood of , the behavior of the sheaf on that small neighborhood should be the same as the behavior of at that point.
Constant sheafIn mathematics, the constant sheaf on a topological space associated to a set is a sheaf of sets on whose stalks are all equal to . It is denoted by or . The constant presheaf with value is the presheaf that assigns to each non-empty open subset of the value , and all of whose restriction maps are the identity map . The constant sheaf associated to is the sheafification of the constant presheaf associated to . This sheaf identifies with the sheaf of locally constant -valued functions on .
Čech cohomologyIn mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Let X be a topological space, and let be an open cover of X. Let denote the nerve of the covering. The idea of Čech cohomology is that, for an open cover consisting of sufficiently small open sets, the resulting simplicial complex should be a good combinatorial model for the space X.
Morphism of algebraic varietiesIn algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also regular is called biregular, and the biregular maps are the isomorphisms of algebraic varieties.
Leray spectral sequenceIn mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays as a special case of the Grothendieck spectral sequence. Let be a continuous map of topological spaces, which in particular gives a functor from sheaves of abelian groups on to sheaves of abelian groups on .
Filtered categoryIn , filtered categories generalize the notion of directed set understood as a category (hence called a directed category; while some use directed category as a synonym for a filtered category). There is a dual notion of cofiltered category, which will be recalled below. A is filtered when it is not empty, for every two objects and in there exists an object and two arrows and in , for every two parallel arrows in , there exists an object and an arrow such that . A filtered colimit is a colimit of a functor where is a filtered category.
Battle of Sept-ÎlesThe Battle of Sept-Îles was a naval action fought on the night of 22/23 October 1943 during World War II as part of the Atlantic campaign. The battle took place off the Sept-Îles near the French coast in the English Channel between a light cruiser and six destroyers of the British Royal Navy hoping to intercept, a German blockade runner, which was accompanied by German torpedo-boat destroyers flotillas of the German Kriegsmarine.
Sept-Îles, QuebecSept-Îles (Quebec French pronunciation : sɛ.t͡s‿ɪl, French for "Seven Islands") is a city in the Côte-Nord region of eastern Quebec. It is among the northernmost locales with a paved connection to the rest of Quebec's road network. The population was 25,686 as of the 2011 Canadian census. The town is called Uashat, meaning "bay" in Innu-aimun. The city is well known for having major iron companies like Iron Ore Company of Canada and the Cleveland-Cliffs mining company. The city relies heavily on the iron industry.
Arthur VerhaegenArthur Théodore Verhaegen (31 August 1847 in Brussels – 5 September 1917 in Elsene) was a Gothic Revival Belgian architect and a politician of the Catholic Party, one of the founders of Belgian Christian democracy. He was a grandson of the politician and lawyer Pierre-Théodore Verhaegen. Verhaegen began his career as a civil engineer at Charleroi. In 1872, after his marriage to Claire Lammens, he moved to Ghent and dedicated himself to arts and crafts in the Gothic Revival style.
EftelingEfteling (ˈɛftəlɪŋ) is a fantasy-themed amusement park in Kaatsheuvel, the Netherlands. The attractions reflect elements from ancient myths and legends, fairy tales, fables, and folklore. The park was opened on May 31, 1952. It evolved from a nature park with a playground and a Fairytale Forest into a full-sized theme park. It now caters to both children and adults with its cultural, romantic, and nostalgic themes, in addition to its wide array of amusement rides including six roller coasters and four dark rides.
Elections in VenetoThis page gathers the results of elections in Veneto. Veneto has always been characterised by the big role played by the Catholic Church and centrist politics, but was also an early stronghold of the Radical Party and the Italian Socialist Party. In 1919, in the first election with male universal suffrage, the Catholic-inspired Italian People's Party won 42.6% of the vote and the Italian Socialist Party 36.2%.
Mahnaz ShiraliDr. Mahnaz Shirali is an Iranian author and political sociologist who is a professor at Science Po university in France. She graduated in architecture engineering from faculty of fine arts of Tehran University in 1992. She moved to France in 1994 where she obtained her PhD in sociology from School for Advanced Studies in the Social Sciences in Paris in 2000. Her PhD thesis was about crisis in youth Iranian generation.
