| 番号 |
著者 |
タイトル・掲載雑誌 |
コメント |
| IJ02 |
M.Intermont/
M.Johnson |
「Model structure on the category of ex-space」.Top.
App.Vol-119. 2002. 325-353 |
ex-categoryのmodel structure |
| Se72 |
G.Segal |
「Categories and cohomology theories」. Top. Vol-13.
1972. 293-312 |
Γ-space、categoryなどの分類空間 |
| SS03 |
S.Schwede/
B.Shipley |
「Stable model categories are categories of
module」.Top. Vol-42. 2003. 103-153 |
stable model categoryに関して |
| Ri89 |
J.Rickard |
「Morita theory for derived categories」. J. Lon.
Math. Soc. (2). Vol-39. 1989. 436-456 |
Derived同値とMorita理論 |
| St63 |
J.Stasheff |
「Homotopy associativity of H-spaces. I, II.」. Trans. Amer. Math. Soc. Vol-108 1963,
275-292 |
A-infty spaceに関する事 |
| IM70 |
N. Iwase/
M. Mimura |
「Higher homotopy associativity」 Algebraic Topology
(Arcata, 1986), 193-220, Lecture Notes in Math. 1370, Springer,
Berlin, 1989 |
A-infty spaceとA-infty mapについて |
| Ba61 |
M.Barratt |
「A note of the cohomology of semigroups」. J. Lon.
Math. Soc. Vol-36. 1961. 496-498 |
半群のcohomology |
| DK80 |
W.Dwyer/
D.Kan |
「Simplicial localization of categories」. J. Pure.
App. Alg. Vol-17. 1980. 267-284 |
simplicial localizationに関すること |
| DK80' |
W.Dwyer/
D.Kan |
「Simplicial localization of categories」. J. Pure.
App. Alg. Vol-18. 1980. 17-35 |
simlicial locarizationをhammocで |
| KD80 |
W.Dwyer/
D.Kan |
「Function complexes in homotopical algebra」. Top.
Vol-19. 1980. 427-440. |
simplicial categoryのhom complexについて |
| Fi93 |
P.Filho |
「Completions and fibrations for topological monoids」.
Trans. Amer. Math. Soc. Vol-340. 1993,
127-147. |
topological monoidのgroup completion |
| La04 |
S. Lack |
「A Quillen model structure for bicategories」
K-Theory. 33(3). 2004. 185-197 |
Bicategoriesのcategoryのmodel structure |
| Wa85 |
F. Waldhausen |
「Algebraic K-theory of
spaces」 LMN. Vol-1126. 1985. 318-419. |
spaceのalgebraic K-theory |
| Sa57 |
I.Satake |
「The Gauss-Bonnet Theorem for V-manifolds」 J Math
Soc Japan. Vol-9, No.4. 1957. 464-492. |
Orbifoldの原文 |
| Se68 |
G.Segal |
「Classifying spaces and spectral sequence」
Inst.Hautes Etudes Sci. Publ Math Vol-34 1968. |
topological categoryの分類空間 |
| Ka58 |
D.Kan |
「Adjoint functors」 Trans. Amer.
Math. Soc. 1958. |
functorのadjoint |
| Ka59 |
D.kan |
「On c.s.s complexes」 Amer J. of Math. 1959. |
simplicial setとsmall category |
| Th80 |
R.Thomason |
「Cat as a closed model category」 Cahiers de
Topologie et Geometrie Differetuielle. Vol-21. 1980, |
small categoryのcategoryのmodel structure |
| St72 |
A.Strom |
「The homotopy category is a homotopy category」
Arch. Math. (Basel), Vol-23. 1972.
435-441. |
位相空間のstrom type model structure |
| Co06 |
M.Cole |
「Mixing model structures」 Topology Appl. Vol-153(7). 2006.
1016-1032. |
model structureのmix |
| Ha74 |
H.Hastings |
「Fibrations of compactly generated spaces」 Michigan Math. J. Vol-21 1974 243-251. |
CGHのmodel structure |
| Gi04 |
J.Gillespie |
「The flat model structure on Ch(R)」 Trans. Amer. Math.
Soc., 356(8). 2004. 3369-3390 (electronic). |
chain complexのflat model structure |
| SV02 |
R.Schwanzl/
R.Vogt |
「Strong cofibrations and fibrations in enriched
categories」 Arch. Math. (Basel),
79(6). 2002. 449-462. |
strom typeのchain complexのmodel structure |
| Qu73 |
D.Quillen |
「Higher algebraic K-theory」. LMN. Vol-341. 1973.
85-147. |
algebraic K-theoryの原点 |
| Ike04 |
K.Ikegami |
「Cobordism group of Morse functions on manifolds」
Hiroshima Math. J. 34(2) : 211-230,
2004. |
Morse functionのcobordism |
| Kal04 |
B.Kalmar |
「Cobordism group of Morse functions on unoriented
surfaces」 Kyushu Journal of Mathematics || 59(2) ||
351-363 |
向きのない曲面上のMorse functionのcobordism |
| Doe93 |
J.Doeraene |
「L.S.-category in a model category.」 J. Pure Appl.
Algebra, 84(3):215-261, 1993. |
Model categoryでのLS-category |
| Has75 |
H. Hastings |
「Fibrations of compactly generated spaces.」 Michigan Math. J., 21:243-251 (1975), 1974.
|
CGHのStrom typeのmodel structure |
| Ste67 |
N. Steenrod. |
「A convenient category of topological spaces.」
Michigan Math. J., 14:133-152, 1967.
|
compact生成空間について |
| DH01 |
W.Dwyer/
H.Henn. |
「Homotopy theoretic methods in group cohomology」
Advanced Courses in Mathematics CRM Barcelona. Birkhauser Verlag,
Basel, 2001. |
homotpopy colimitとGrothendick contructionなど |
| Seg78 |
G.Segal |
「Classifying spaces related to foliations」
Topology, Vol. 17, pp.367-382, 1978 |
monoidの分類空間など |
| Cho03 |
B.Chorny |
「The model category of maps of spaces is not
cofbrantly generated」 Proc. Amer. Math.
Soc., 131(7):2255-2259 (electronic), 2003. |
cofibranty generatedでないmodel structureについて |
| Tho79 |
R.Thomason |
「Homotopy colimits in the category of small category」
Math. Proc. Comb. Phil. Soc. Vol85,pp91-109. 1979 |
homotopy colimitに関する基本 |
| BK72 |
A. Bousfield/
D.. Kan |
「Homotopy limits,
completions and localizations」
volume 304 of Lecture Notes in
Mathematics. Springer-Verlag, Berlin, 1972 |
homotopy limitに関する基本 |
| Vog73 |
R. Vogt |
「Homotopy limits and colimits」. Math. Z., 134:11-52, 1973. |
homotopy (co)limitの原文 |
| Vog77 |
R.Vogt |
「Commuting homotopy limits」. Math. Z., 153(1):59?82, 1977 |
homotopy colimit、limitの可換性 |
| HV92 |
J. Hollender/
R. Vogt, |
「Modules of topological spaces, applications to
homotopy limits and E_infty structures」, Arch. Math. 59
(1992), 115-129 |
homotopy limit colimitのbar constructionによる特徴づけ |
| Mey84 |
J.P. Meyer |
「Bar and cobar constructions」, J. Pure Applied
Alg., 33, (1984), 163-207 |
bar constructionの一般化 |
| Pup74 |
V. Puppe |
「A Remark on ``Homotopy Fibration''」. Manuscripta
Math. 12 (1974), pp. 113--120 |
fibrationとhomotopy colimit |
| May75 |
P.May |
「Classifying Spaces and Fibrations」 AMS Memoirs
155. 1975 |
bar constructionなどのhomotopy |
| Cur71 |
Edward B. Curtis |
. 「Simplicial homotopy theory」. Advances in Math.,
6:107-209 (1971), 1971. |
simplicial setにまつわること |
| Qui68 |
Daniel G. Quillen |
「The geometric realization of a Kan fibration is a
Serre fibration」 Proc. Amer. Math.
Soc., 19:1499-1500, 1968 |
Kan fibrationの実現はSerre fibration |
| And78 |
D. W. Anderson. |
「Fibrations and geometric realizations」. Bull. Amer. Math.
Soc., 84(5):765-788, 1978. |
実現とfibrationの関連。groupoidのmodel構造 |
| Qui69 |
Daniel Quillen |
「Rational homotopy theory」. Ann.
of Math. (2), 90:205-295, 1969. |
有理ホモトピー論のさきがけ |
| BG76 |
A.Bousfield/
V.Gugenheim |
「On PL DeRham Theory and Rational Homotopy
Type」,AMS Memoirs 1976; 94 pp;Volume: 8 |
有理ホモトピー論のホモトピー論 |
| THT00 |
A.Gomez-Tato/
S.Halperin/
D. Tanre |
.「Rational homotopy theory for non-simply connected
spaces」 Trans. Amer. Math. Soc., 352(4):1493-1525,
2000. |
単連結で無い場合の有理ホモトピー論 |
| Bau89 |
Hans Joachim Baues. |
「Algebraic homotopy」,
volume 15 of Cambridge Studies in
Advanced Mathematics. Cambridge University Press, Cambridge,
1989. |
fibration category、cofibration category |
| FRS95 |
R.Fenn/
C.Rourke/
B. Sanderson |
「Trunks and classifying spaces」. Appl. Categ. Structures, 3(4):321?356,
1995. |
Trunkとその分類空間 |
| Joy82 |
David Joyce |
「A classifying invariant of knots, the knot quandle.」
J. Pure Appl.
Algebra, 23(1):37?65, 1982. |
Quandleを用いたknotの計算 |
| FR92 |
Roger Fenn/
Colin Rourke. |
「Racks and links in codimension two.」 J. Knot Theory Rami?cations 1(4):343?406,
1992. |
Rackを用いたlinkの計算 |
| Min02 |
Elias Gabriel Minian |
「Cat as a Λ-cofibration category.」 J. Pure Appl.
Algebra, 167(2-3):301-314, 2002. |
CatのΛ-cofibration structure |
| JT91 |
Andre Joyal /Myles Tierney |
「Strong stacks and classifying spaces. In Category theory」, volume 1488 of LNM., pages 213-236.
Springer, Berlin, 1991. |
Catのfolk model structure |
| Min03 |
Elias Gabriel Minian |
「Loop and Suspension Functors for Small Categories and
Stable Homotopy Groups」. Applied Categorical Structures 11(2):
207-218 (2003) |
Catにおけるloop and suspension functorとhomtopy群の定義 |
| Min00 |
Elias Gabriel Minian |
「Generalized Cofibration Categories and Global
Actions」K-Theory Volume 20, Number 1 / 2000 |
Λ-cofibration categoryについて |
| Min02' |
Elias Gabriel Minian |
「Λ-Cofibration Categories and the Homotopy Categories
of Global Actions and Simplicial Complexes」. Applied Categorical
Structures 10(1): 1-21 (2002) |
Min02と似た内容 |
| Min05 |
Elias Gabriel Minian |
「Numerably Contractible Categories」 K-Theory Volume
36, Numbers 3-4 / 2005 |
CatにおけるCW complex |
| Min02'' |
Elias Gabriel Minian |
「Complexes in Cat」 Topology and its Applications
Volume 119, Issue 1, 31 March 2002, Pages 41-51 |
CatにおけるCW complex |
| Gol81 |
M.Golasinski |
「Homotopies of small
categories」Fund. Math.,CXIV(1981), 209-217
|
Catのcubical setに関連したhomotopy |
| Gol79 |
M.Golasinski |
「The category of cubical set and the category of small
categories」 Bulletin de l'academie polonaise des seiences VOl
XXVII No.11-12,1979 |
small categoryのcubical nerveについてのお話 |
| CELH |
Carmen/
Elvira-Donaza/
Luis-Javier/
Hernandez-Paricio. |
「Closed model categories for the n-type of spaces and simplicial sets」. Math. Proc. Cambridge Philos. Soc.,
118(1):93?103, 1995. |
位相空間とsimplicial setのn-type model structure |
| Goo90 |
Thomas G. Goodwillie. |
「Calculus. I. The first derivative of pseudoisotopy theory.」
K-Theory,
4(1):1-27, 1990. |
Goodwillie's calculus part 1 |
| Goo92 |
Thomas G. Goodwillie. |
「Calculus. II. Analytic functors.」 K-Theory,
5(4):295-332, 1991/92. |
Goodwillie's calculus part 2 |
| Goo03 |
Thomas G. Goodwillie. |
「Calculus. III. Taylor series.」 Geom. Topol.,
7:645-711 (electronic), 2003. |
Goodwillie's calculus part 3 |
| Wei95 |
Michael Weiss. |
「Orthogonal calculus.」 Trans. Amer. Math.
Soc., 347(10):3743-3796, 1995. |
Godwillie's calculusの変形版orthogonal calculus |
| La02 |
Stephen Lack |
A Quillen model structure for 2-categories, K-Theory
26:171-205, 2002 |
2-categoryのcategoryのfolk model structure |
| BC03 |
M. Bullejos/
A. M. Cegarra |
On thegeometry of s-categories and their classifying spaces,
K-Theory 29:211-229, 2003 |
2-categoryにおけるQuillen's Theorem A |
| Sal87 |
Mario Salvetti |
Topology of the complement of real hyperplanes in CN .
Invent. Math. , 88(3):603-618,
1987. |
Salvetti complexの構成 |
|
For95 |
Robin. Forman |
Morse theory for cell
complexes |
Discrete Morse theoryの原点 |
| Bro73 |
Kenneth S. Brown |
Abstract Homotopy Theory and Generalized Sheaf
Cohomology,Transactions of the American Mathematical Society,
Vol. 186 (1973), 419-458 |
Fibration categoryにおけるhomotopy
pullbackについて |
| DJ91 |
M. Davis, T. Januszkiewicz |
Convex polytopes, Coxeter orbifolds and torus actions,Duke Math. J. 62 (1991), no. 2, 417--451 |
準トーリック多様体の原点 |