Subject: categories: Omega categories paper from Carl Futia

From: [email-masked]
Date: Fri, 9 Apr 2004 13:59:37 EDT

I've  just completed a paper entitled "Omega Categories I". The abstract
appears below.

I am trying to post this paper on the math archive but haven't yet succeeded
because I lack an adademic affiliation.

In the meantime anyone who would like a copy may obtain one from me upon
request. I'll send it to you as an uncompressed Postscript file attached to an
e-mail message.

Carl Futia

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ABSTRACT:
We develop a theory of weak omega categories that will be accessible to
anyone who is familiar with the language of categories and functors and who has
encountered the definition of a strict 2-category.

The most remarkable feature of this theory is its simplicity. We build upon
an idea due to Jaques Penon by defining a weak omega category to be a span of
omega magmas with certain properties. (An omega magma is a reflexive, globular
set with a system of partially defined, binary composition operations which
respects the globular structure.)

Categories, bicategories, strict omega categories and Penon's weak omega
categories are all instances of our weak omega categories. We offer a heuristic
argument to justify the claim that Batanin's weak omega categories also fit into
our framework.

We show that the Baez-Dolan stabilization hypothesis is a direct consequence
of our definition of weak omega categories.

We define a natural notion of a psuedo-functor between weak omega categories
and show that it includes the classical notion of a homomorphism between
bicategories. In any weak omega category the operation of composition with a fixed
1-cell defines such a psuedo-functor.

Finally, we define a notion of weak equivalence between weak omega categories
which generalizes the standard definition of an equivalence between ordinary
categories.