Homotopy Limit Functors on Model Categories and Homotopical Categories

By W. Dwyer. 2005

268 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dfe04809ec5566bfd979a90775b22b75e6f53730

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homotopy Theory of Higher Categories: THE MODEL STRUCTURE (2010, methodology): “They discussed the model category for simplicial categories on a fixed set of objects in a series of papers [89] [90] [91]; but it wasn’t until some time later with their unpublished manuscript with Hirschhorn [87], which subsequently became [88], and then Bergner’s paper [33] that the global case w”
Fibrations and Yoneda's lemma in an ∞-cosmos (2017, background): “As usual, we shall assume that W contains all isomorphisms and satisfies the 2-of-6 property [10] and that F also contains all isomorphisms and is closed under composition.”
On the nonexistence of elements of Kervaire invariant one (2009, methodology): “Equipped with the stable weak equivalences, the category SG becomes a homotopical category in the sense of [23], and so both the homotopy category ho SG and the functor SG → ho SG are defined.”
Derived algebraic geometry (2014, methodology): “gory L(M) always has 15 limits and colimits, and moreover that these limits and colimits in L(M) can be computed using the well known homotopy limits and homotopy colimits of homotopical algebra (see [Dwye-Hirs-Kan-Smit] for a general discussion about homotopy limits and colimits). The ∞-category of”
Quasi-categories vs Segal spaces (2006, methodology): “Segal categories were first introduced by Dwyer, Kan and Smith [DKS], where they are called special ∆o-diagrams of simplicial sets .”
Triangulated surfaces in triangulated categories (2013, background): “Here, the assumption that C is combinatorial, can be relaxed (the concept of homotopy limits can be defined in much greater generality [DHKS04]).”
Higher Segal Spaces (2012, background): “However, as shown in [DHKS04], derived limit functors always exist: any model category is homotopically complete (and cocomplete).”