Homology (同调 ) in Geometry & Topology

https://frankliou.wordpress.com/2011/10/07/幾何與拓樸簡介/

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https://frankliou.wordpress.com/2011/11/21/同調論/
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同胚” homomEophism (eg. Donnut 和茶壶), 可以扭捏泥土从前者变后者。

“同态” (同样形态homomOrphism), 就是Same-Shape-ism. eg. (相似) Similar Triangle.

如果是congruent (全等), 就是 Isomorphism (“同构“, 同样结构)。

所有新加坡人自己人批评自己人kiasu, 其实大家都kiasu, 因为是”自同态” (自己同样态度kiasu), 自=”Endo”
=> Endomorphism.

如果猪八戒照镜子, 看到镜子里面的丑八怪, 还是他猪八戒,
=> Automorphism “自同构” (镜里的影子和自己同样结构)

这些构造(structure)在WW1后被当时Structurism哲学思想影响, Bourbaki 法国师范大学一批学生 (犹太人 André Weil是领袖)把全部人类的数学重写, 以structures (Set, Group, Ring, Module, Field, Vector Space, Topology. .. )为基础 就是新(抽象)数学, 影响到今。
WW2 后, 美国人Sanders MacLane 更上一层楼, 把Set/Group/Ring…等structures 再归类成Category (范畴), 研究其共通的性质 (Morphism 动态), 能够 举一反十。应用在IT 里, 其 Category 就是Functional programming, Types…

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