?ュ??瀛﹁??锛?Hideto Asashiba

?ュ??????浣?锛?????澶у?/浜??藉ぇ瀛 楂?绛???绌堕??/span>

?ュ???堕?达?2024骞?1??5? 涓??? 14:30-16:30

?ュ???扮?癸?寤鸿?烘ゼ209

?ュ????瑕?锛?Throughout this talk G is a fixed group, and k is a fixed field.  All categories are assumed to be k-linear.

First, we give a systematic way to induce G-precoverings by adjoint functors using a 2-categorical machinery. Now let C be a skeletally small category with a G-action, C/G the orbit category of C, (P, \phi) : C ??> C/G the canonical G-covering, and mod C, mod C/G the categories of finitely generated modules over C, C/G, respectively.

Then there exists a canonical G-precovering (P., \phi.) : mod C ??> mod C/G.

We then apply this machinery to produce G-precoverings (mod C)/S ??> (mod C/G)/S?? between the factor categories or localizations of mod C and mod C/G from the precovering (P., \phi.).

This is further applied to the morphism category H(mod C) of mod C to have a G-precovering fp(K) ??> fp(K??) between suitable subcategories K and K?? of the categories of finitely presented modules over mod C and mod C/G, respectively.

This is a joint work with Rasool Hafezi and Mohammad Hossein Keshavarz.

?ュ??瀛﹁??绠?浠?锛?Hideto Asashiba???????ユ??????澶у??ｈ???浼?????锛?浜??藉ぇ瀛︽?板???绌朵腑蹇?涓?澶ч???绔?澶у?????绌跺????2024骞存?ユ???板?浼?浠ｆ?板?濂????峰??????ㄥ??虹?浠风???????规?????绌跺??寰?浜?涓?绯诲????褰卞??????缁??????朵腑?充?Grothendieck??????瀵煎?虹?浠风??缁?????琛ㄥ??/span>Adv. Math. 235(2013), 134-160???ㄥ??虹?浠枫??绋冲?绛?浠蜂?Gabriel 瑕?????璁虹?稿?虫?归?㈢????绌讹?澶?浜???娌垮?颁?????浠??充?寰?????娆¤???????寸??瀵煎?鸿???寸??绮?????Grothendieck????????浣?宸茬?瀹???锛?涓?涓?姝ワ???浠??涓?姝ョ??绌惰??归?㈢???稿?抽?????甯?????璇?ideto Asashiba????锛?甯???????ideto Asashiba?????ㄥ??虹?浠蜂?瑕?????璁虹????????缁?楠?锛??ㄥ??虹?浠蜂?瑕?????璁虹??绌剁兢璁恒??