From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2919 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: further references on semi-categories Date: Tue, 29 Nov 2005 10:14:51 +0100 (CET) Message-ID: <200511290914.jAT9EpI3003111@fb04209.mathematik.tu-darmstadt.de> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018983 6362 80.91.229.2 (29 Apr 2009 15:29:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:43 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Nov 30 15:04:51 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Nov 2005 15:04:51 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EhX7a-0001yx-Fr for categories-list@mta.ca; Wed, 30 Nov 2005 14:56:02 -0400 X-Mailer: ELM [version 2.4ME+ PL100 (25)] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 64 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:2919 Archived-At: In order to provide a categorical semantics of typed $\lambda$-calculus without $\eta$-rule Susumu Hayashi used semicategories in MR0841025 (87i:18005) Hayashi, Susumu Adjunction of semifunctors: categorical structures in nonextensional lambda calculus. Theoret. Comput. Sci. 41 (1985), no. 1, 95--104. This was later taken up by R.Hoofman in his Thesis on "Nonstable Models of Linear Logic" (see the first 7 items when you type in "Hoofman, R*" in Math.Reviews). However, in my opinion for the purpose of modelling $\lambda\beta$-calculus it is more natural to use the following kind of structures: (small) categories \C with finite products such that y(Y)^{y(X)} (taken in Psh(\C)) is a retract of some y(E). Thomas Streicher