29 мар. 2024 г. · The homotopy coherent nerve (also called simplicial nerve) of a simplicially enriched category is a simplicial set which includes information ... Definitions · Examples and illustrations · Related concepts

An online resource for homotopy-coherent mathematics.

2 мар. 2020 г. · We can redefine the classical nerve of a category C as the simplicial set. Fun(−,C) : ∆op → Set. A motivating example for the homotopy coherent ...

29 апр. 2010 г. · The homotopy coherent nerve of a simplicial category C C is the simplicial set with ℕ C n = \mathbb{N} C_n = sSet-Cat ( ℂ Δ n , C ) (\mathbb{C}\ ...

5 февр. 2024 г. · Instead of solving the problem one category at a time, we identify an appropriate homotopy coherent generalization of the notion of a category ...

other homotopy then a functors from the ordinary commutative square cubeshould correspond precisely to homotopy coherent squares cubes. So now our goal is to ...

The simplicial set [n] 7− → HomCat∆ (G([n]),C) is called the homotopy coherent nerve of a simplicial enriched category C, denoted as a functor N : Cat∆ −→ sSet.

4 авг. 2022 г. · In this paper, we construct a homotopy coherent nerve for (\infty,n)-categories. We show that it realizes a right Quillen equivalence between ...

7 мар. 2012 г. · (Here we are using that on a discrete operad P P the homotopy coherent dendroidal nerve trivially coincides with the ordinary dendroidal nerve N ...

24 янв. 2024 г. · In the case of (∞, 1)-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched ...