The concepts category, functor, and natural transformation were introduced (in reverse order) during the early 1940s by Samuel Eilenberg and Saunders Mac Lane, aiming at resolving certain conceptual problems in algebraic topology. Before explaining in detail the points concerned, it might be useful ...
From spaces and continuous maps, we constructed graded abelian groups and homomorphisms. We now cast this construction in the more general language of category theory. Definition1.A categoryCconsists of the following data. ﹡﹡a class ob(C)of objects; ...
Algebraic topology, Category theoryhomological algebraThis talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship (2002-2004) by the speaker and Rafael Sivera (Valencia). The aim ...
相关的英语类的工作跟文献还有 Jardine 的 Categorical Homotopy Theory ,里面主要是借助一般的 presheaf category 上的同伦结构来研究 cubical model 的同伦结构。 presheaf 的范畴有一类非常漂亮的性质,即它是一个 elementary topos,即它具有 limit、colimit、subobject classifier,以及它是 Cartesian closed。尤其是这...
代数拓扑哈彻答案-Algebraic-Topology-Solutions 热度: LECTURE1:CATEGORYTHEORY Categorytheoryisverydry.Itisneverthelessausefullanguagetospeakof certainthings. 1.Categories Definition1.1.Acategoryconsistsof: (1)AcollectionofobjectsObC. (2)Foranypairofobjectsx,y∈ObC,asetofmorphismsMap ...
09 Interactions between topology and algebra_ advances in algebraic K-theory 53:34 About Irreversibility in Rarefied Gas Dynamics 54:26 General Relativity, Differential Geometry and Differential Equations; Stories Fr 56:46 Indigenous Knowledge in STEM Education 1:09:27 Random walks and graphs in ...
Spanier也是在他的书最前面一部分内容里面解释了代数拓扑学科的特点,他说他写的这本名为Algebraic Topology的教科书本来是要被称为Functorial Topology的。因为这个学科本身就是在研究一个个从拓扑空间到某个代数结构的函子。从某种意义上来说,这个学科其实一直在对空间分类。这个会在后面的学习过程中有更深入的体会。
代 数拓扑 Algebraic Topology (Part 1/3) Excellent Advanced Math Lecture Series (Part 1 to 3) by齊震宇老師 (2012.09.10) Part I: History:1900 H. Poincaré invented Topologyfrom Euler Characteristic (V -E + R = 2) Motivation of Algebraic Topology :FindInvariants[1]of various topological ...
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Saunders Mac Lane was an American mathematician who was a cocreator of category theory, an architect of homological algebra, and an advocate of categorical foundations for mathematics. Mac Lane graduated from Yale University in 1930 and then began gradua