From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/216 Path: news.gmane.org!not-for-mail From: Venanzio Capretta Newsgroups: gmane.science.mathematics.categories Subject: Re: Where does the term monad come from? Date: Wed, 01 Apr 2009 20:47:12 +0100 Message-ID: Reply-To: Venanzio Capretta NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1238677393 15614 80.91.229.12 (2 Apr 2009 13:03:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 2 Apr 2009 13:03:13 +0000 (UTC) To: Thorsten Altenkirch , Original-X-From: categories@mta.ca Thu Apr 02 15:04:31 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LpMaq-0008KB-Vs for gsmc-categories@m.gmane.org; Thu, 02 Apr 2009 15:04:29 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LpLne-0003Qr-Rk for categories-list@mta.ca; Thu, 02 Apr 2009 09:13:38 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:216 Archived-At: The philosopher Gottfried Leibniz believed that every entity in the Universe is a separate substance that doesn't interact with others. He called these substances "monads". All properties and events that happen to a monad are implicit in its nature from its creation. So if an apple falls from a tree and bounces off my head, there is actually no contact: the apple-monad bounces by itself without the help of my head and the Venanzio-monad feels pain without the intervention of the apple. All monads are synchronized from creation by the wisdom of God. This implies that every monad has an internal representation of every entity in the universe and these representations can never influence objects outside the monad. The analogy with our monads should be evident! Thorsten Altenkirch wrote: > A question just came up at the Midland Graduate School (actually in > the functional programming lecture): > Where does the word monad come from? > > I know that a monad is a monoid in the category of endofunctors, but > what is the logic monoid => monad? > > Btw, I frequently encounter monads in a categories of functors which > are not endofunctors. An example are finite dimensional vectorspaces > which can be constructed via a monoid in the category of functors > FinSet -> Set, here I is the embedding and (x) can be constructed from > the left kan extension and composition. > The unit is given by the Kronecker delta and join can be constructed > from Matrix multiplication. Should one call these beasts monads as > well? Is there a good reference for this type of construction? > > Cheers, > Thorsten > >