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.

Footnotes

↑1 | c.f. Algebraic Topology by Allen Hatcher. |
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