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 ...
Computational Algebraic Topology 热度: 相关推荐LECTURE1:CATEGORYTHEORY Categorytheoryisverydry.Itisneverthelessausefullanguagetospeakofcertainthings. 1.Categories De,nition1.1.Acategoryconsistsof: (1)AcollectionofobjectsObC. (2)Foranypairofobjectsx,y∈ObC,asetofmorphismsMapC(x,y). ...
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...
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 spaces (in higher dimension). 求拓扑空间的“...
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。
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...
These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and...
Maximilien Péroux Visiting Assistant Professor Michigan State University I am a Visiting Assistant Professor at Michigan State University. My postdoctoral mentor is Teena Gerhardt. My main interests are Algebraic Topology, Stable Homotopy Theory, Algebraic K-theory, Higher Category Theory, and Theoretical...
Mathematics - Algebraic TopologyMathematics - Category Theory55U4018C35We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category A has a model structure that is left-induced from that on A. In particular it follows that any presentable model ...
in Algebraic Topology’ and is referred to herein as [SSAT]. There is also a third book in progress, on vector bundles, characteristic classes, and K–theory, which will be largely independent of [SSAT] and also of much of the present book. This is referred to as [VBKT], its provisio...