From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/399 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Announcement: paper on linear functors available Date: Wed, 11 Jun 1997 11:53:15 -0300 (ADT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016943 25580 80.91.229.2 (29 Apr 2009 14:55:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:43 +0000 (UTC) To: categories Original-X-From: cat-dist Wed Jun 11 11:53:17 1997 Original-Received: by mailserv.mta.ca; id AA29920; Wed, 11 Jun 1997 11:53:15 -0300 Original-Lines: 38 Xref: news.gmane.org gmane.science.mathematics.categories:399 Archived-At: Date: Wed, 11 Jun 1997 10:13:43 -0400 From: Robert A. G. Seely We wish to announce the availability of the following paper. Linearly distributive functors by J.R.B. Cockett R.A.G. Seely ABSTRACT This paper introduces a notion of "linear functor" between linearly distributive categories that is general enough to account for common structure in linear logic, such as the exponentials (!, ?), and the additives (product, coproduct), and yet when interpreted in the doctrine of *-autonomous categories, gives the familiar notion of monoidal functor. We show that there is a bi-adjunction between the 2--categories of linearly distributive categories and linear functors, and of *-autonomous categories and monoidal functors, given by the construction of the "nucleus" of a linearly distributive category. We develop a calculus of proof nets for linear functors, and show how linearity accounts for the essential structure of the exponentials and the additives. This paper was first presented at a conference held in Montreal in May 1997, in honour of Michael Barr's 60th birthday, and is dedicated to him in celebration of this occasion. ------------------------ The paper may be found at the following URLs or from the WWW home page Contact if there is any problem retrieving this paper.