La versión en línea de la de cerrar la entrada de los Informes de la Midwest Categoría Seminario IV (1970, Springer LNM 137) cuesta $29.95 por lo que decidí poner una transcripción aquí.
CATEGORICALLY, THE FINAL EXAMINATION
------------- ---------------------
FOR THE
SUMMER INSTITUTE AT BOWDOIN COLLEGE (Maine) 1969
'I thought I saw a garden door that opened with a key,
I looked again and found it was a Double Rule of Three,
And all its mysteries, I said, are plain as day to me.'
(Verse by the true founder of
Category Theory)
Important Instruction: This is a take-home exam:
--------------------- Do not bring it back!
Answer as many as possible at a time.
1. Are foundations necessary? To put it another way, given a
chance, wouldn't Mathematics float?
2. Describe the category of foundations. Is this a concrete cate-
gory? A re-enforced concrete category?
3. Discuss the relations and limitations of the foundations set
forth by:
a) Frege-Russell
b) Bernays-Gödel
c) Playtex.
4. (Mac Lane's Theorem) Prove that every diagram commutes.
5. Considering a left-adjoint as male and a right adjoint as female,
give the correct term for a contravariant functor self-adjoint
on the right.
6. Considering a left-adjoint as husband and right-adjoint as
wife, give a precise definition of "marital relations". Do the
same for the pre-adjoint situation.
7. Discuss the Freudian significance of exact sequences. (Hint:
consider the fulfillment by one arrow of the kernel of the next.)
8. Find two new errors in Freyd's "Abelian Categories".
--- ===
9. Trace the origin of the Monads-Triads-Triples controversy to the
important paper of St. Augustine.
10. Using theorems from both Freyd and Mitchell, prove that every
reflective category is co-reflective. Dualize.
11. Give your opinion of the following exercises:
a) Ten pushouts
b) Twenty laps around an adjoint triangle
c) Two supernatural transformations.
12. Write out at least one verse of
a) "Little Arrows"
b) "Doing What Comes Naturally"
c) "Hom on the Range"
13. Why is the identity functor on 2 called the "Mother Functor"?
-
14. Write down the evident diagram, apply the obvious argument, and
obtain the usual result. (If you can't do it, you're not
looking at it hard enough, or, perhaps, too hard.)
Phreilambud
PS
Después de cierta controversia en los comentarios acabo de google para "quién es phreilambud" y encontré esto:
Date: Mon, 3 Oct 2005 11:58:38 -0400 (EDT)
From: Peter Freyd <pjf@saul.cis.upenn.edu>
To: categories@mta.ca
Subject: categories: Re: Phreilambud at Bowdoin 1969
``Phreilambud'' was written by me, a young student named Lambert who
disappeared, I think, from mathematics and David Eisenbud, now paying
for his sins as head of MSRI (Berkeley).
Peter
PPS Otra cosa que vino a mi mente, aunque no es exactamente lo que pide la pregunta, pero estrechamente relacionado con el anterior. Jack Duskin una vez me dijo que después de que uno de sus discursos en simplicial conjuntos, con la pizarra llena de docenas de paralelo manojos de flechas que se pegue en todas las direcciones detrás de él, alguien de la audiencia le advirtió de los riesgos de compartir el destino de San Sebastián.
