Useful discussion in
Halliday, M.A.K. (1988). On the Ineffability of Grammatical Categories. James D. Benson, Michael J.Cummings and William S. Greaves (eds.) Linguistics in a Systemic Perspective. (CILT39). Amsterdam/ Philadelphia: John Benjamins, 27-51.
Otherwise, yes, linguists seem to assume grammatical classes across languages, that are defined semantically to some extent. Eg attached figure (Rose & Martin 2012) could apply to all the languages I know of.
 To be clear, Halliday (1988) says nothing about the relation between semantic categories and grammatical classes across different languages (the subject of Othman's query). Instead, it is concerned, on the one hand, with explaining why functional grammatical categories, such as Subject, cannot be theorised by decoding them from above (by reference to what they realise) and, on the other hand, with identifying ways around the problem, which in SFL, means encoding them from below (by reference to what realises them).
 To be clear, this figure is intended to represent relations between discourse semantic categories and grammatical classes. Each of the five realisation relations can be examined in turn.
- Attitude realised by adjective. The problem here is that the congruent realisation of attitude is not limited to the word class 'adjective', as demonstrated, for example, by the attitudinal potential of 'idiot' (noun), 'stupidly' (adverb), and 'deceive' (verb).
- Entity realised by nominal group. The problem here is that, in the discourse semantic model, the term 'entity' is not a general category, but only features as a subtype of Range (Martin 1992: 309-11; Martin & Rose 2007: 96). For Halliday & Matthiessen (1999: 177), the experiential semantic element congruently realised by the nominal group is 'participant'.
- Event realised by verbal group. The problem here is that, in the discourse semantic model, the term 'event' is grammatical, not discourse semantic (Martin 1992: 325; Martin & Rose 2007: 97).
- Figure realised by clause. This is true, but misleading, because the term 'figure', and its congruent relation with the clause, do not derive from Martin's (1992) discourse semantic model, but from the ideational semantics of Halliday & Matthiessen (1999).
- Activity sequence realised by clause complex. In the ideational semantics of Halliday & Matthiessen (1999: 49), it is the sequence that is congruently realised as a clause complex. In Martin (1992: 321-5), activity sequences are located in field, the ideational dimension of context misconstrued as register. In Martin & Rose (2007: 76), activity sequences are reinterpreted as discourse semantic: as an experiential system, IDEATION, Martin's misunderstanding and rebranding of Halliday's textual system of lexical cohesion, inter alia. For the theoretical inconsistencies in activity sequences in Martin (1992), see here; for theoretical inconsistencies in IDEATION in Martin (1992), see here.