It's well known that Dold-Kan correspondence is an isomorphism between simplicial vector spaces and non-negative chain complexes of vector spaces. Moreover, weak equivalences and fibrations are ...
Related to this question, I would like to know, if there is an explicit presentation of the $(\infty,1)$-category of a model category of abelian chain complexes, but this time in terms of simplicial ...
One of the common definitions of homology using the singular chains, i.e. maps from the simplex into your space. The free abelian group on these can be made into a chain complex and one can take the ...