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  1. Newsgroups: fj.sci.math
  2. Path: sparky!uunet!stanford.edu!sun-barr!sh.wide!wnoc-kyo!kuis!kudpc!nucc!d43013a
  3. From: d43013a@nucc.cc.nagoya-u.ac.jp (Yukihiko Namikawa)
  4. Subject: Re: Topos (Re: Q in int. math.)
  5. Message-ID: <1992Dec22.144309.22451@nucc.cc.nagoya-u.ac.jp>
  6. Organization: School of Natural Sciences, Nagoya University, Nagoya, Japan.
  7. References: <MIYOSHI.92Dec22014028@gala.slab.sfc.keio.ac.jp> <SATOSHI.92Dec22174011@whale.math.ryukoku.ac.jp> <MIYOSHI.92Dec22215655@gala.slab.sfc.keio.ac.jp>
  8. Distribution: fj
  9. Date: Tue, 22 Dec 1992 14:43:09 GMT
  10. Lines: 46
  11.  
  12. $BL>8E20$NO2@n$G$9!#(B
  13.  
  14. In article <MIYOSHI.92Dec22215655@gala.slab.sfc.keio.ac.jp> miyoshi@slab.sfc.keio.ac.jp (Hiroyuki Miyoshi) writes:
  15. >
  16. >$B7DXfBg3X$N;09%$G$9!%(B
  17. >
  18. >$B7wO@E*?dO@$r9T$J$&;~$K(Bsmallness$B$O=EMW$G$9$,!$(Bfibered/indexed category
  19. >$B$d(Btopos$B$G5DO@$9$l$P8+$+$1>e$"$($FFCDj$N=89gO@$K4T85$7$J$/$F$b$=$l$J$j(B
  20. >$B$N$3$H$,$G$-$^$9!%!J$H$$$C$F$bFC$K?t3X$NJ}$G$O$3$N$"$?$j$"$^$j$h$/8&5f(B
  21. >$B$5$l$F$$$k$H$O$$$($J$$$h$&$G$9$,!K!%(B
  22. >
  23. >$B$`$7$m!$Be?t4v2?$G$I$N$h$&$J=89g$K;}$A9~$`I,MW$,$"$k$N$+(B
  24. >$B!JNc$($PB>$NJ,Ln$N7k2L$rMxMQ$7$?$j$9$k;~$K!K$K$h$k$N$G$7$g$&!%(B
  25. >$BBe?t4v2?$K>\$7$$J}!$$I$&$G$7$g$&$+!)(B
  26. >$B;d$OBe?t4v2?$b=89gO@$b$h$/CN$i$J$$$N$G!$(B
  27. >$B7wO@!J$HO@M}!K$G5DO@$G$-$?$[$&$,5$;}$A$$$$$G$9!%(B
  28.  
  29. $B>\$7$$$+$I$&$+$O$H$b$+$/!"0l1~Be?t4v2?$r@lLg$K$9$k?M4V$H$7$F!"(B
  30. $B$I$&$b$*Ez$($7$J$$$H$$$1$J$$$h$&$J$N$G!#(B
  31. $B$H$$$C$F$bBe?t4v2?$NJ}$G$O!"$=$&?<$$9M$($,$"$C$F8@$C$F$$$k$o$1$G$O$J$/!"(B
  32. $BA0AX(B(presheaf)$B$r(Bcontravariant functor$B$H$7$FDj5A$7$F$7$^$C$?$N$G!"(B
  33. $BNc$($PA0AX4V$N(Bmorphism$B$,=89g$K$J$k$h$&$K!"$=$7$FI,MW$JA`:n!J6K8B$r<h$C$?$j(B
  34. $B$J$I!K$O<+M3$K$G$-$k$h$&$K!"$3$N$h$&$J>l$r@_Dj$7$?$@$1$G$9!#(B
  35.  
  36. In article <SATOSHI.92Dec22174011@whale.math.ryukoku.ac.jp>
  37. satoshi@whale.math.ryukoku.ac.jp (Satoshi Kobayashi) writes:
  38. >
  39. >$B$=$l$K$7$F$b!"Be?t4v2?$N$h$&$JIaDL$N?t3X$N$?$a$K!"K\Ev$K$=$s$J$KBg$-$J(B 
  40. >universe $B$,I,MW$J$N$+$J$"!#$b$C$H>.$5$$$N$G==J,$8$c$J$$$+!"$H$$$&5$$,(B
  41. >$B$9$k$1$l$I!#(B
  42. >
  43.  
  44. $B=89gO@$+$iHt$S=P$5$J$$HO0O$G$G$-$k$@$1<+M3$K$$$m$$$m$NA`:n$,(B
  45. $B$G$-$k$h$&!"$"$i$+$8$a==J,$KBg$-$J$b$N$r$H$C$F$*$$$?$H$$$&$3$H$G$9!#(B
  46. $B$=$l$r$I$3$^$G>.$5$/$G$-$k$+$H$$$&$3$H$O!"4pACO@$NJ}$NLdBj$G!"(B
  47. $B2f!9Be?t4v2?$r$d$k?M$NLdBj0U<1$K$O!JIaDL!K$"$j$^$;$s!#(B
  48. $B!VBg$O>.$r7s$M$k!W$G$9!#(B
  49. $B$^$"Be?t4v2?3X$K=P$F$/$k(BGrothendieck$B0LAj$G$O!"(Bcovering family$B$r;H$C$F(B
  50. $BDj5A$G$-$k$b$N$P$+$j$J$N$G!"4JC1$J(Bfibred category$B$N5DO@$G==J,$G$9!#(B
  51. $B$7$+$7(BGrothendieck$B$K$OBe?t4v2?3X$@$1$G$J$/!"A4?t3X$rJq3g$9$k?t3X$r(B
  52. $BE83+$7$h$&$H$$$&Bg$-$JL4$,$"$C$?$N$G$O$J$$$+$H;W$$$^$9!#(B
  53. -- 
  54.    *   *   *     *                $@O2@n!!9,I'(J
  55.     * *    * *   *                $@L>8E20Bg3XM}3XIt?t3X65<<(J
  56.      *     *   * *                d43013a@nucc.cc.nagoya-u.ac.jp
  57.      *     *     *                namikawa@math.nagoya-u.ac.jp
  58.