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Peter Freyd: "Properties Invariant Within Equivalence
Types of Categories", a.k.a. [Freyd76]
In 1976 Peter Freyd published a short paper called "Properties Invariant Within Equivalence Types of Categories" in a
book called "Algebra, Topology, and Category Theory - a Collection of
Papers in Honor of Samuel Eilenberg". Its two first paragraphs say:
All of us know that any "mathematically relevant" property on
categories is invariant within equivalence types of categories.
Furthermore, we all know that any "mathematically relevant" property
on objects and maps is preserved and reflected by equivalence
functors. An obvious problem arises: How can we conveniently
characterize such properties? The problem is complicated by the fact
that the second mentioned piece of common knowledge, that
equivalence functors preserve and reflect relevant properties on
objects and maps, is just plain wrong.
I first met Sammy in the fall of 1958 and within ten minutes he
was selling me on a "stylistic" point that turns out to be the
central clue to the problem. (How often Sammy's "stylistic" points
have totally changed entire mathematical viewpoints!) It took me 16
years to make the connection.
Its diagrammatic language - that later became the basis for Freyd
and Scedrov's book "Categories, Allegories", published in 1990 -
totally changed my own way of thinking.
For many years that paper from 1976 was very hard to find, even in
the standard unofficial sites - so I scanned my photocopy of it and
made it available here:
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