From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10308 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Christian Williams Newsgroups: gmane.science.mathematics.categories Subject: Closed Grothendieck Construction Date: Wed, 21 Oct 2020 12:43:27 -0700 Message-ID: Reply-To: Christian Williams Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="33531"; mail-complaints-to="usenet@ciao.gmane.io" To: categories@mta.ca Original-X-From: majordomo@rr.mta.ca Thu Oct 22 18:13:55 2020 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1kVdDv-0008aH-BV for gsmc-categories@m.gmane-mx.org; Thu, 22 Oct 2020 18:13:55 +0200 Original-Received: from rr.mta.ca ([198.164.44.159]:40746) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1kVdAt-00043S-UM; Thu, 22 Oct 2020 13:10:47 -0300 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1kVd6P-0006tJ-H5 for categories-list@rr.mta.ca; Thu, 22 Oct 2020 13:06:09 -0300 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10308 Archived-At: Hello, The equivalence of monoidal indexed categories and monoidal fibrations has been proved in "Monoidal Grothendieck Construction" by Joe Moeller and Christina Vasilakopoulou. (https://arxiv.org/abs/1809.00727) Has the analogous statement for closed structure been proved? It appears to be folklore, often assumed in categorical logic and elsewhere. It is likely that I simply haven't found the right reference. Any help is appreciated. Thank you, Christian Williams [For admin and other information see: http://www.mta.ca/~cat-dist/ ]