This expository article sets forth a self-contained and purely algebraic proof of a deep result
of Quillen stating that the category of simplicial commutative algebras over a commutative …

For a commutative ring $ A $, we have the category of (bounded-below) chain complexes of
$ A $-modules $ Ch_ {+}(A\mymod) $, a closed symmetric monoidal category with a …

We put a Quillen model structure on the category of small categories enriched in simplicial $
k $-modules and non-negatively graded chain complexes of $ k $-modules, where $ k $ is a …

Extending previous work, we define monoidal algebraic model structures and give
examples. The main structural component is what we call an algebraic Quillen two-variable …

In this paper, we introduce a strategy for studying simplicial commutative algebras over
general commutative rings R. Given such a simplicial algebra A, this strategy involves …

Motivated by knot theory, we introduce a homology theory for small categories with functor
coefficients. Under this general framework, different familiar homology theories such as …

We give a category theoretic approach to several known equivalences from (classic) tilting
theory and commutative algebra. Furthermore, we apply our main results to establish a …

We study the simplicial coalgebra of chains on a simplicial set with respect to three notions
of weak equivalence. To this end, we construct three model structures on the category of …

For an arbitrary simplicial complex K, Davis and Januszkiewicz have defined a family of
homotopy equivalent CW–complexes whose integral cohomology rings are isomorphic to …

Building upon Hovey's work on Smith ideals for monoids, we develop a homotopy theory of
Smith ideals for general operads in a symmetric monoidal category. For a sufficiently nice …