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Stream: learning: questions

Topic: nerve of a natural transformation.

ADITTYA CHAUDHURI (Aug 29 2021 at 16:07):

We know that there is a standard embedding called nerve $N: \rm{Cat} \hookrightarrow \rm{sSet}$ from the 1-category of categories to the category of simplicial sets. We also know that $\rm{Cat}$ can be considered as a 2-category by including the natural transformations. Is there a way we can describe these natural transformations in terms of the elements of sSets, by appropriately giving a 2-category structure on sSets? Do we then have to consider the nerve of 2-categories?

Emilio Minichiello (Aug 29 2021 at 19:16):

A natural transformation between two functors of categories induces a homotopy of the maps on respective nerves

ADITTYA CHAUDHURI (Aug 29 2021 at 19:18):

Ahh! I got it!! Thanks!

Emilio Minichiello (Aug 29 2021 at 19:19):

No problem!