Structural attribution of fundamental complexes in category terms

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 [1]c.f. Algebraic Topology by Allen Hatcher. for example that clarifies what portion of data gives rise to the distinction in the simplicial model.


1 c.f. Algebraic Topology by Allen Hatcher.