A MathOverflow Question about Second Duals of Vector Spaces

April 6, 2014

I asked a question about second duals of vector spaces on MathOverflow.

Thank you for letting me know if you have any idea.


Iterated Dual Vector Spaces

March 29, 2014

I’ve posted a question on Mathematics Stack Exchange about iterated dual vector spaces.

Any idea? Thanks in advance!

Selected Texts

June 26, 2013

I put together four short texts I have written.

New version of my text about “Categories and Sheaves”

April 29, 2013

The last version of my text about the book “Categories and Sheaves” by Kashiwara and Schapira is available on this page of my website and on figshare: pdftex.

Function of a Matrix

June 15, 2012

New version of Function of a Matrix.

Two Tiny Texts

April 28, 2012

Here are two new tiny texts:

Yoneda’s Lemma

PDF version to print

PDF version for e-readers



PDF version to print

PDF version for e-readers


Function of a Matrix

March 27, 2012
My last text. Available
* from my website
* as an MSE post
* from WordPress

Categories and Sheaves by Masaki Kashiwara and Pierre Schapira (2)

March 22, 2012

On page 24, line 4, one reads

Hom_C(X,Y) \in U for all X,Y \in C, …

This is incorrect (I think).

* Google Books Preview
* Amazon Preview

PS. This has already been pointed out by Joseph Oesterlé:


Categories and Sheaves by Kashiwara and Schapira.

February 25, 2012

Started reading Categories and Sheaves, by Masaki Kashiwara and Pierre Schapira.


Links: Google Books — Amazon.

Two Excerpts from “Set Theory and the Continuum Hypothesis” by Paul Cohen

August 6, 2011
It should be emphasized that these functions are “real” mathematical objects and not objects of any formal system … [Section I.7, p. 26.]

The theorems of the previous section are not results about what can be proved in particular axiom systems; they are absolute statements about functions. [Section I.9, p. 39.]