Comments for The Unapologetic Mathematician
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Mathematics for the interested outsiderThu, 26 May 2016 06:43:31 +0000hourly1http://wordpress.com/Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30457
Thu, 26 May 2016 06:43:31 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30457I think I’ll try work at it again.Thanks!
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30456
Thu, 26 May 2016 06:41:28 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30456Here is my argument: The left quadrilateral gives $\rho_{(A\bigotimes B)\bigotimes1}=\rho_{(A\bigotimes B)}\bigotimes1.$
]]>Comment on Mac Lane’s Coherence Theorem by John Armstrong
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30449
Wed, 25 May 2016 17:31:28 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30449If you want to work out a chain of equal morphisms more explicitly, it might help to remember that the associator and the right identor are both natural isomorphisms, so they can be inverted to point the other way.
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30448
Wed, 25 May 2016 16:58:15 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30448Yes I know that this is what we are trying to prove, but my question is can you little bit elaborate on it. I was trying to prove it by starting from the lower left corner to the top corner of the triangle and then using in various ways three naturality quadrilaterals. I was unable to use the top triangle identities, and thus couldn’t prove that the central triangle commutes.
]]>Comment on Mac Lane’s Coherence Theorem by John Armstrong
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30447
Wed, 25 May 2016 14:22:03 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30447That the triangle near the center commutes is exactly what we’re proving here. The whole outer pentagon commutes, by the pentagon identity, and then we can tile in with various commuting squares and triangles until we get down to the triangle we want to verify.
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30446
Wed, 25 May 2016 06:43:17 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30446I can’t see why the triangle near the center commute
]]>Comment on Cotangent Vectors, Differentials, and the Cotangent Bundle by What is a coordinate function $x^i$ of a manifold, given a chart $(U,x)$? - MathHub
https://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundle/#comment-30397
Sun, 08 May 2016 20:12:34 +0000http://unapologetic.wordpress.com/?p=8866#comment-30397[…] I am trying to understand the notes here: https://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundl…. […]
]]>Comment on More on tensor products and direct sums by Proving that tensor distributes over biproduct in an additive monoidal category - MathHub
https://unapologetic.wordpress.com/2007/04/17/more-on-tensor-products-and-direct-sums/#comment-30313
Fri, 08 Apr 2016 10:26:45 +0000http://unapologetic.wordpress.com/2007/04/17/more-on-tensor-products-and-direct-sums/#comment-30313[…] found a similar proof in the setting of modules (https://unapologetic.wordpress.com/2007/04/17/more-on-tensor-products-and-direct-sums/) but unfortunately he glosses over the part where I am stuck. At least I seem to be considering the […]
]]>Comment on Isomorphisms of Vector Spaces by Isomorphisms of inner-product spaces - MathHub
https://unapologetic.wordpress.com/2008/10/17/isomorphisms-of-vector-spaces/#comment-30312
Thu, 07 Apr 2016 11:42:51 +0000http://unapologetic.wordpress.com/?p=1697#comment-30312[…] I think I understand why all finite-dimensional vector spaces over a field $mathbb{K}$ are isomorphic to $mathbb{K}^n$. Any linear map $T: V rightarrow W$ between finite-dimensional vector spaces taking a basis to a basis is automatically an isomorphism, by linearity. (c.f. this nice post.) […]
]]>Comment on Clairaut’s Theorem by Existence of mixed partials in Clairaut's theorem. - MathHub
https://unapologetic.wordpress.com/2009/10/15/clairauts-theorem/#comment-30295
Sun, 03 Apr 2016 03:27:10 +0000http://unapologetic.wordpress.com/?p=3763#comment-30295[…] only after the assumption that both mixed partials exist and are continuous. In this blog post here, the author proves a stronger […]
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