From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10746 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Ivan Di Liberti Newsgroups: gmane.science.mathematics.categories Subject: ItaCa Fest - Coraglia and Kock - 19 May Date: Mon, 16 May 2022 12:30:35 +0200 Message-ID: Reply-To: Ivan Di Liberti Mime-Version: 1.0 (Mac OS X Mail 16.0 \(3696.80.82.1.1\)) Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="38306"; mail-complaints-to="usenet@ciao.gmane.io" To: categories@mta.ca Original-X-From: majordomo@rr.mta.ca Mon May 16 23:16:56 2022 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1nqi5I-0009hx-2i for gsmc-categories@m.gmane-mx.org; Mon, 16 May 2022 23:16:56 +0200 Original-Received: from rr.mta.ca ([198.164.44.159]:60030) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1nqi3N-0004FP-Bh; Mon, 16 May 2022 18:14:57 -0300 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1nqi34-0007IO-56 for categories-list@rr.mta.ca; Mon, 16 May 2022 18:14:38 -0300 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10746 Archived-At: Dear all, The next date of the ItaCa Fest will be May 19, 2022 at 3 pm (Italian = time): - G. Coraglia, - J. Kock. The zoom link is the following: = https://stockholmuniversity.zoom.us/j/68792232558 While the Fest website is this one: = https://progetto-itaca.github.io/pages/fest22.html Join us (and bring a friend)! Cheers, Beppe, Ivan, Edoardo, Fosco, Paolo. = =E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2= =80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80= =94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94= =E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2=80=94=E2= =80=94=E2=80=94=E2=80=94 Coraglia. Title: Comonads for dependent types Abstract: In exploring the relation between a classical model of = dependent types (comprehension categories) and a new one (judgemental = dtts) we pin-point the comonadic behaviour of weakening and contraction. = We describe three different 2-categories and show that they are = 2-equivalent, then proceed to analyze the benefits of each of the three. = The fact that one can precisely relate such different perspectives = allows, for example, for a swift and cleaner treatment of type = constructors: we show how certain categorical models for dependent types = come inherently equipped with some due to the choices one makes in = introducing tools to interpret context extension. Kock. Title: Decomposition spaces, right fibrations, and edgewise subdivision Abstract: Decomposition spaces are simplicial infinity-groupoids subject = to an exactness condition weaker than the Segal condition. Where the = Segal condition expresses composition, the weak condition expresses = decomposition. The motivation for studying decomposition spaces is that = they have incidence coalgebras and M=C3=B6bius inversion. The most = important class of simplicial maps for decomposition spaces are the CULF = maps (standing for 'conservative' and = 'unique-lifting-of-factorisation'), first studied by Lawvere; they = induce coalgebra homomorphisms. The theorem I want to arrive at in the = talk says that the infinity-category of (Rezk-complete) decomposition = spaces and CULF maps is locally an infinity-topos. More precisely for = each (Rezk-complete) decomposition space D, the slice infinity-category = Decomp/D is equivalent to PrSh(Sd(D)), the infinity-topos of presheaves = on the edgewise subdivision of D. Most of the talk will be spent on = explaining preliminaries, though. This is joint work with Philip Hackney. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]