Date: Mon, 27 Nov 1995 16:20:30 -0400 (AST)
Subject: adjunction question

Date: Mon, 27 Nov 1995 11:59:10 -0800 (PST)
From: Andrew Ensor <ensor@math.berkeley.edu>

I was wondering if anyone could provide me with some information on the
following:
  Suppose <F,G,eta,epsilon>:A -> B is an adjunction and let C denote
  the collection of all possible finite horizontal compositions of
  F,G (as identity natural transformations),eta, and epsilon.
  So, for example the horizontal composite epsilon.F.eta
  is a natural transformation in C.
  I am interested in knowing more about vertical compositions using members
  of C. For example the vertical composite of epsilon.F with F.eta is
  epsilon.F.eta, and the vertical composite of epsilon.F.G.F with
  epsilon.F.eta.eta is epsilon.epsilon.F.eta.eta.
  Must C be closed under all possible vertical compositions?
Any assistance or reference would be appreciated.
Sincerely,
Andrew Ensor.