Subject: categories: film functor

From: Peter Freyd <[email-masked]>
Date: Thu, 13 Jul 2000 16:33:03 -0400 (EDT)

The Dutch film "Antonia" written and directed by Marleen Gorris won
the 1996 Oscar for best foreign language film. There's a scene in
which the 20-year-old granddaughter of the title character is at a
blackboard with a lot of exact sequences. She says (quoting the
English subtitles):

  We will assume that the singular chain complex of the empty set
  equals zero. With theorem 5.8 this implies that the nth homology
  group is the same as the nth relative homology group if we take the
  subspace as the empty set. New we can construct a functor from the
  category....from the category Top to the category of chain 
  complexes. Define the functor  S*  as follows: S*  sends the ordered
  pair  <X,A>  to the singular chain complex of the space  X  divided 
  by the complex of  A.

Is this the first commercial film with categories and functors? (It's
not the first with homological algebra: in 1980 "It's My Turn" opened
with its lead at a blackboard proving the snake lemma.)

It should be noted that the categories and functors in "Antonia" turn
out to be foreplay: the speaker makes eye contact with a guy in her
audience and the next scene instantly transports them from the
classroom to the bedroom.