A Thomason model structure on categories detects weak equivalences through a simplicial nerve and compares their homotopy
theory with that of spaces. In the higher-dimensional formulation, the right
adjoint is 
,
where 
is the Street nerve and 
is right adjoint to simplicial subdivision. Its left adjoint
is 
,
where 
is the categorification functor and 
is subdivision.
Thomason Model Structure
See also
Grothendieck Homotopy Hypothesis, Model Category, Quillen Equivalence, Simplicial SetExplore with Wolfram|Alpha
References
Ara, D. and Maltsiniotis, G. "Towards a Thomason Model Structure on the Category of Strict
-Categories." Adv. Math. 259, 557-654, 2014.
https://doi.org/10.1016/j.aim.2014.03.013.
Cite this as:
Weisstein, Eric W. "Thomason Model Structure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThomasonModelStructure.html