Second term is \sum k_\alpha \sigma_{x_0} = [\sum k_\alpha] \sigma_{x_0} = 0 \sigma_{x_0} = 0. The sum of the coefficients is zero since we are working with something in the kernel of the augmentation map. You can't do that factoring out of the \sigma's in the first term since the \sigma_\alpha's are all different \alpha's.
@@uttarandutta4376 , use mathematical language rather than using personal adjective. Can you explain why it is "abstract nonsense" ?? It is ofcourse"abstract" but with "sense". Understand ?
@@Adivasilover10 Just look it up on wiki. This a fairly common term. Referring to a joint paper with Samuel Eilenberg that introduced the notion of a "category" in 1942, Saunders Mac Lane wrote the subject was 'then called "general abstract nonsense"'.
you know how hard it is when the musical symbols start appearing
Homotopy Invariance starts at 1:07:00
This is the best lecture
Truth
Great! please upload cohomology and homotopy theory. Thanks!
Agreed! Would really like to see the second semester of this course!
This may seem like completely useless math, but Homology could be used to generate structural models of proteins, for instance.
At 42:50 minute, I didn't understand why $\sum k_{\alpha}=0$ for the 2nd term but not for the first term ? Any explanation
Second term is \sum k_\alpha \sigma_{x_0} = [\sum k_\alpha] \sigma_{x_0} = 0 \sigma_{x_0} = 0. The sum of the coefficients is zero since we are working with something in the kernel of the augmentation map. You can't do that factoring out of the \sigma's in the first term since the \sigma_\alpha's are all different \alpha's.
@@thanderhop1489 , thanks
Girl at 45:19 is GORGEOUS
37:10
Abstract nonsense!
@RickScience Abstract nonsense is actually a term used to describe Category Theory. It's not an insult.
@@arkapointer , I didn't listen such term applied to a mathematical talk.
@@Adivasilover10 look it up dude, it indeed is.
@@uttarandutta4376 , use mathematical language rather than using personal adjective. Can you explain why it is "abstract nonsense" ?? It is ofcourse"abstract" but with "sense". Understand ?
@@Adivasilover10 Just look it up on wiki. This a fairly common term. Referring to a joint paper with Samuel Eilenberg that introduced the notion of a "category" in 1942, Saunders Mac Lane wrote the subject was 'then called "general abstract nonsense"'.