Martin's Register And Genre: Context Or Co-text?

Are Martin's register and genre, modelled as strata, theorised on the notion of context or co-text?

Halliday (2007 [1991]: 271):

Originally, the context meant the accompanying text, the wording that came before and after whatever was under attention. In the nineteenth century it was extended to things other than language, both concrete and abstract: the context of the building, the moral context of the day; but if you were talking about language, then it still referred to the surrounding words, and it was only in modern linguistics that it came to refer to the non-verbal environment in which language was used. When that had happened, it was Catford, I think, who suggested that we now needed another term to refer explicitly to the verbal environment; and he proposed the term “co-text”.

Martin, in describing his model of stratification, writes (1992: 496):

… the size of the circles also reflects the fact that the analysis tends to focus on larger units as one moves from phonology to ideology.  Thus the tendency at the level of phonology to focus on syllables and phonemes, at the level of lexicogrammar to focus on the clause, at the level of discourse semantics to focus on an exchange or "paragraph", at the level of register to focus on a stage in a transaction, at the level of genre to focus on whole texts …

As this quote makes clear, Martin’s ‘context’ refers to levels within language — and so to co-text, not context — since 'a stage in a transaction' and 'whole texts' are units of language.