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Jul
7 |
comment |
What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
The problems in understanding mathematical English, even in formally written papers, is well described in the book The Language of mathematics, by Mohan Ganesalingam, and many other examples are given in my website athttp://www.abstractmath.org/MM/MMLangMath.htm |
Jun
16 |
awarded | Yearling |
Sep
24 |
awarded | Autobiographer |
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. |