Categorists, Is there a commonly accepted language for infinitary compositions? Here's the sort of thing i'm thinking about. There's a purely syntactic correspondence between a 'braced' notation and an infix notation for composition. Suppose we have a categorically-friendly notion of composition, say c. (Meaning the entities c composes can be viewed as morphisms in a category and c the categorical composition.) Then we can just as easily write - f c g -- c is merely making notationally explicit the interpretation of 'o' in f o g -- we're coloring the 'o', as it were or - {c| f, g |c} -- we've moved from infix to (not quite) prefix notation for the composition. The braced notation, however, is suggestive of a very powerful notational mechanism, comprehension notation. We could easily imagine a language allowing expressions of the form {c| pattern | predicate |c} which would denote pattern{subst_1} c pattern{subst_2} c ... where subst_i is a substition for 'variables' in the pattern of entities satisfying the predicate. This would allow reasoning over infinitary compositions by providing an intensional view of their interior structure. Surely, such a widget has already been invented. Can someone give me a reference? Best wishes, --greg -- L.G. Meredith Managing Partner Biosimilarity LLC 806 55th St NE Seattle, WA 98105 +1 206.650.3740 http://biosimilarity.blogspot.com