We sometimes want to restrict the scope of objects depending on what subject we are dealing with, roughly between the two poles of theory and application. To such a subject where we can reduce significant complexities by choosing a proper “model”, formulated by model category in the sense that they capture the underlying properties that can be evaluated in a derived category, we expectedly can give a good / counter – example of peculiar phenomena in the subject.
In order to successfully reduce a “model”, we want to know what can be discarded or what cannot out of the structural factor of the “model”. This poses on more general optimization problem in such a way that if exists, what is the minimal requirements of well-represented (model) category insensitive to given noises.
In such direction, we share a short writing of simplicial set c.f. Algebraic Topology by Allen Hatcher. for example that clarifies what portion of data gives rise to the distinction in the simplicial model.