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math.AT2025
Thomason-Type Model Structures on Simplicial Complexes and Graphs
Emilio Minichiello
In this paper we show that the Matsushita model structure on loop graphs, which is right-transferred from the Kan-Quillen model structure on simplicial sets, factors through two ot…
math.AT2023
A detailed look at the Szczarba map
Emilio Minichiello, Manuel Rivera, Mahmoud Zeinalian
We explain how to derive an explicit formula for a natural transformation relating the (left adjoints of) the homotopy coherent nerve and the Dwyer-Kan simplicial classifying space…
math.AT2022★ 2 cited
Categorical models for path spaces
Emilio Minichiello, Manuel Rivera, Mahmoud Zeinalian
We establish an explicit comparison between two constructions in homotopy theory: the left adjoint of the homotopy coherent nerve functor, also known as the rigidification functor,…