on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
A cartesian model category (alias cartesian closed model category) is a cartesian closed category that is equipped with the structure of a monoidal model category in a compatible way, which combines the axioms for a monoidal model category and an enriched model category.
A cartesian model category (following Rezk (2010) and Simpson (2012)) is a cartesian closed category equipped with a model structure that satisfies the following additional axioms:
(Pushout-product axiom). If $f : X \to Y$ and $f' : X' \to Y'$ are cofibrations, then the induced morphism $(Y \times X') \cup^{X \times X'} (X \times Y') \to Y \times Y'$ is a cofibration that is trivial if either $f$ or $f'$ is.
(Unit axiom). The terminal object is cofibrant.
the standard Quillen model structure on topological spaces on compactly generated weakly Hausdorff topological spaces is cartesian closed
the standard model structure on simplicial sets is cartesian closed.
cartesian closed category, locally cartesian closed category
cartesian closed model category, locally cartesian closed model category
cartesian closed (∞,1)-categorylocally cartesian closed (∞,1)-category
Charles Rezk, A cartesian presentation of weak $n$-categories. (2010). (arXiv:0901.3602)
Carlos Simpson, Homotopy theory of higher categories (2012)
Last revised on March 21, 2021 at 20:16:13. See the history of this page for a list of all contributions to it.