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Published online by Cambridge University Press: 08 January 2010
Once Theofilos was […] painting a mural in a Mytilene baker's shop […] As was his habit, he had depicted the loaves of bread upright in their trays, like heraldic emblems on an out-thrust shield – so that no one could be in any doubt that they were loaves of bread and very fine ones, too. The irate baker pointed out that in real life loaves thus placed would have fallen to the floor. ‘No,’ replied Theofilos – surely with that calm, implacable self-certainty which carried him throughout what most people would call a miserable life – ‘only real loaves fall down. Painted ones stay where you put them.’
The Athenian (1980)In the next two chapters we explore one possible definition of weak ω-category. Its formal shape is very simple: we take the category ε of globular sets and the free strict ω-category monad T on ε, construct a certain T operad L, and define a weak ω-category to be an L-algebra.
In order to see that this is a reasonable definition, and to get a feel for the concepts involved, we proceed at a leisurely pace. The present chapter is devoted to contemplation of the monad T (Section 8.1), of T -operads (= globular operads, Section 8.2), and of their algebras (Section 8.3). In Chapter 9 we define the particular globular operad L and look at its algebras – that is, at weak ω-categories. To keep the explanation in this chapter uncluttered, the discussion of the finite-dimensional case (n-categories) is also deferred to Chapter 9; we stick to ω-categories here.
Globular operads are an absolutely typical example of generalized operads.
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