author | Kevin Walker <kevin@canyon23.net> |
Sun, 25 Sep 2011 14:44:38 -0600 | |
changeset 889 | 70e947e15f57 |
parent 848 | 7dc75375d376 |
child 905 | 7afa2ffbbac8 |
permissions | -rw-r--r-- |
764
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
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1 |
Changes between arXiv version 2 and arXiv version 3 |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
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2 |
--------------------------------------------------- |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
3 |
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5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
4 |
Many small clarifications of text. |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
5 |
|
823 | 6 |
Many typos corrected. |
764
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
7 |
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779 | 8 |
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764
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
9 |
The most significant changes are: |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
10 |
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5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
11 |
- added to acknowledgements |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
12 |
- clarified definition of splittable |
779 | 13 |
- changed to pitchfork notation for splittable subsets of fields |
764
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
14 |
- added definition of collaring homeomorphism |
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
15 |
- improved definition of bordism n-category |
781
0a9adf027f47
rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents:
773
diff
changeset
|
16 |
- fixed definition of a refinement of a ball decomposition (intermediate manifolds should also be disjoint unions of balls) |
767 | 17 |
- added brief definition of monoidal n-categories |
764
5a2594504cac
delta file for next arXiv/G&T version (complete as of now, but will need to be updated)
Kevin Walker <kevin@canyon23.net>
parents:
diff
changeset
|
18 |
- fixed statement of compatibility of product morphisms with gluing |
767 | 19 |
- added remark about manifolds which do not admit ball decompositions; restricted product theorem (7.1.1) to apply only to these manifolds |
770
032d3c2b2a89
added remark about defect categories; tweaked sphere cat intro
Kevin Walker <kevin@canyon23.net>
parents:
767
diff
changeset
|
20 |
- added remarks about categories of defects |
772
73fc4868c039
string diagrams have stratifications more general than mere cell complexes
Kevin Walker <kevin@canyon23.net>
parents:
770
diff
changeset
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21 |
- clarified that the "cell complexes" in string diagrams are actually a bit more general |
773
775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
|
22 |
- added remark to insure that the poset of decompositions is a small category |
786
91d32d0cb2ef
corrected statement of module to category restrictions; note that this affects the numbering of items in subsection 6.4
Kevin Walker <kevin@canyon23.net>
parents:
782
diff
changeset
|
23 |
- corrected statement of module to category restrictions |
788
6a1b6c2de201
more reorganization of n-cat defs
Kevin Walker <kevin@canyon23.net>
parents:
786
diff
changeset
|
24 |
- reduced intermingling for the various n-cat definitions (plain, enriched, A-infinity) |
790
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
788
diff
changeset
|
25 |
- strengthened n-cat isotopy invariance axiom to allow for homeomorphisms which act trivially elements on the restriction of an n-morphism to the boundary of the ball |
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
788
diff
changeset
|
26 |
- more details on axioms for enriched n-cats |
792
966a571daa10
added remark on super algebra
Kevin Walker <kevin@canyon23.net>
parents:
790
diff
changeset
|
27 |
- added details to the construction of traditional 1-categories from disklike 1-categories (Appendix C.1) |
794
24f14faacab4
finished topological case of Appendix B
Kevin Walker <kevin@canyon23.net>
parents:
792
diff
changeset
|
28 |
- extended the lemmas of Appendix B (about adapting families of homeomorphisms to open covers) to the topological category |
797
40729de8e067
finish fam-o-homeo axiom revisions and discussion
Kevin Walker <kevin@canyon23.net>
parents:
794
diff
changeset
|
29 |
- modified families-of-homeomorphisms-action axiom for A-infinity n-categories, and added discussion of alternatives |
845
c9b55efd79dd
added splittability axiom for fields
Kevin Walker <kevin@canyon23.net>
parents:
823
diff
changeset
|
30 |
- added n-cat axiom for existence of splittings, and added similar axiom for fields |
802
e3ddb8605e32
adding transversality requirement to product morphism axiom
Kevin Walker <kevin@canyon23.net>
parents:
800
diff
changeset
|
31 |
- added transversality requirement to product morphism axiom |
805 | 32 |
- added remarks on Morita equivalence for n-categories |
786
91d32d0cb2ef
corrected statement of module to category restrictions; note that this affects the numbering of items in subsection 6.4
Kevin Walker <kevin@canyon23.net>
parents:
782
diff
changeset
|
33 |
- rewrote definition of colimit (in "From Balls to Manifolds" subsection) to allow for more general decompositions; also added more details |
847
50088eefeedf
remark about families of collar maps acting; misc
Kevin Walker <kevin@canyon23.net>
parents:
845
diff
changeset
|
34 |
- added remark about families of collar maps acting on the blob complex |
848
7dc75375d376
fixing proof of 7.1.1 (product thm)
Kevin Walker <kevin@canyon23.net>
parents:
847
diff
changeset
|
35 |
- small corrections to proof of product theorem (7.1.1) |
7dc75375d376
fixing proof of 7.1.1 (product thm)
Kevin Walker <kevin@canyon23.net>
parents:
847
diff
changeset
|
36 |
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