Wednesday
28
February
2024

Speaker:
Professor Hans Porst,
Universität Bremen

Time:
13:00

Venue:
Mathematics Division, Room 1006

In this talk I will discuss the relation between two theorems
and their proofs: the older one is due to Pierre Samuel (1948), the newer one
to Peter Freyd (1964). While Samuel’s result is hardly known at all, Freyd’s
is (one of) the most important theorems of elementary category theory —
known as Freyd’s Adjoint Functor Theorem.
Both results provide constructions which can be applied to quite a number of non-trivial situations in different areas of mathematics as, e.g., the existence of free topological groups or the Stone-Cech-compactification. Thus, ˇ
the obvious question is: How are these related? The somewhat surprising answer to this question is: Though Freyd’s result is more general then
Samuel’s, their proofs are essentially the same — up to the language of
mathematics available to the authors. Thus, they show by example what
Wittgenstein expressed by writing “The limits of my language are the limits
of my world“.
Because of this I will start my talk (maybe taking owls to Athens) by
briefly recapitulating the development of the language of mathematics during the first half of the 20th century.
**For the category theorists:** An alternative title of this talk, thus,
could have been (explaining why I present it this year): Does the GAFT
turn 60 this year, or turned it 75 already last year?