The horizontal line notation was introduced by Gerhard Gentzen in his logical sequent calculus. If a set of formulas S implies a and b, then S implies a/\b and vice-versa which was written as: S |- a,b ______ S |- a/\b Going from top to bottom was conjunction-introduction, and going in the other direction was conjunction-elimination. After Lawvere noted that these Gentzen rules were simple adjunctions, he started writing all adjunctions using this Gentzen-style notation with the two adjoint transposes on top and on bottom and the arrow replacing the turnstile ( |- ) symbol. The notation caught on. __________________ David Ellerman Visiting Scholar University of California at Riverside Email: david@ellerman.org Webpage: www.ellerman.org View my social science research on my SSRN Author page: http://ssrn.com/author=294049 View my mathematics research at: http://arxiv.org/find/math/1/au:+Ellerman_D/0/1/0/all/0/1 Now out in paperback: Helping People Help Themselves: From the World Bank to an Alternative Philosophy of Development Assistance. University of Michigan Press. 2006. For more information, see the table of contents: http://www.ellerman.org/Davids-Stuff/Books/NEW%20RELEASE%20NOTICE.pdf . Book available at better booksellers online. -----Original Message----- From: categories@mta.ca [mailto:categories@mta.ca] On Behalf Of PETER EASTHOPE Sent: Sunday, March 15, 2009 8:36 AM To: categories@mta.ca Subject: categories: Horizontal line notation. Lawvere & Schanuel use a horizontal line notation. Page 326 for example. X --> 1^T --------- TxX --> 1 This is unfamiliar. Does the line have a name? How is it read? I'll guess either "(X --> 1^T) is equivalent to (TxX --> 1)" or "(X --> 1^T) is isomorphic to (TxX --> 1)". Thanks, ... Peter E. -- http://members.shaw.ca/peasthope/ http://carnot.yi.org/ = http://carnot.pathology.ubc.ca/