Thomason'un homotopi eşlimit teoremi ve kategorilerin kohomolojisi

In 1978, R.W. Thomason proves that for any functor from a small category to the category of small categories, there is a homotopy equivalence between the homotopy colimit construction of the functor and the Grothendieck construction of the functor. We prove that Grothendieck construction is a precofibred category over the canonical functor from Grothendieck construction to the small category. We also prove that for any functor between small categories, there is a homotopy equivalence between the homotopy colimit of left comma categories and the nerve of the domain category. We show that these two together prove Thomason's homotopy colimit theorem from a conceptual point of view. We further investigate how our conceptual approximation for the proof of Thomason's homotopy colimit theorem becomes useful for the cohomology version of Thomason's theorem which was proven by A. M. Cegarra in 2020.