bio | website | sixwingedseraph.wordpress.com |
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location | Saint Paul, Minnesota, USA | |
age | ||
visits | member for | 4 years, 11 months |
seen | Sep 3 at 16:42 | |
stats | profile views | 411 |
Charles Wells. Professor Emeritus of Math at Case Western Reserve University. Websites:
http://www.abstractmath.org/Word%20Press/ http://www.abstractmath.org/ http://www.cwru.edu/artsci/math/wells/home.html
Feb 8 |
accepted | If $a$ is irrational, must $a^a$ be irrational? |
Feb 6 |
asked | If $a$ is irrational, must $a^a$ be irrational? |
Oct 26 |
awarded | Good Answer |
Nov 11 |
awarded | Nice Answer |
Oct 14 |
awarded | Yearling |
Jan 24 |
awarded | Nice Answer |
Oct 15 |
awarded | Yearling |
Apr 28 |
awarded | Good Answer |
Nov 28 |
awarded | Nice Answer |
Oct 15 |
awarded | Yearling |
Aug 15 |
comment |
Graphical representation of mathematical structures (in the spirit of unified modeling language)
A specific technique in category theory for building structures is outlined in Graph Based Logic and Sketches, by Atish Bagchi and Charles Wells, arxiv.org/abs/0809.3023. This was specifically designed to be translated easily into an object-oriented program. |
Aug 14 |
comment |
Is there a notion of congruence relation for essentially algebraic structures?
Some colimits blow up even with algebraic theories. For example, the underlying set of the coproduct of two groups in the category of groups is not the coproduct (disjoint sum) of the underlying sets. |
Aug 13 |
comment |
Collapsing objects in a category
My answer to Peter Arndt's question contains some information about this question. |
Aug 13 |
comment |
Is there a notion of congruence relation for essentially algebraic structures?
Congruences on categories work very nicely when restricted to bijections on objects. This has attracted a lot of interest. Extension Theories for Categories, by Charles Wells. cwru.edu/artsci/math/wells/pub/pdf/catext.pdf For the following references I thank Peter Webb: An Introduction to the Representations and Cohomology of Categories, by Peter Webb. math.umn.edu/~webb/Publications/CategoryAlgebras.pdf G. Hoff, Cohomologies et extensions de categories, Math. Scand. 74 (1994), 191--207. H.-J. Baues and G. Wirsching, Cohomology of small categories, JPAA 38 |
Aug 13 |
revised |
Is there a notion of congruence relation for essentially algebraic structures?
Added info about effective equivalence relations. |
Aug 13 |
answered | Is there a notion of congruence relation for essentially algebraic structures? |
Jul 31 |
comment |
Question on the decimal expansion of algebraic numbers
If you can give a precise statement of "not too many small periodic blocks in a row" that would apparently be a counterexample to Borel's conjecture. But Borel's conjecture may have a more precise statement that rules this out. |
May 11 |
comment |
What does “kernel” mean in integral kernel?
I wrote about this question here: sixwingedseraph.wordpress.com/2010/05/12/… |
Feb 8 |
comment |
Your favorite surprising connections in Mathematics
This is the observation that should have occurred to everyone first! (It didn't to me either.) It is so familiar we forget how amazing it is. |
Jan 8 |
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Classification of properties of structures
Read about sketches in Johnstone's book Sketches of an Elephant (second volume). They give a hierarchy going down from your number (1) -- geometric logic, essentially algebraic logic (finite-limit theories), algebraic logic. There are many variations. There is undoubtedly no end to such classifications, both up and down from first order logic. |