Combinators, as defined originally by Moses Schönfinkel, give rise to a Turing-complete model of computation. This paper presents a diagrammatic representation of combinators as presheaves defined over a category of generic figures. We adopt Sergeyev’s grossone numeral system, which, together with our categorical representation of combinators, ensures a sharper characterization of non-halting combinators. As a result of our analysis, we show how certain “infinite” combinators can be recast in the grossone formalism using the notion of observability, which captures the general concept of tractable properties of sequences with length less than or equal to grossone.