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Answer by Ronnie Brown for Grothendieck's Homotopy Hypothesis - Applications...
Since "Pursuing Stacks" was "written in English in response to a correspondence in English" I feel I ought to explain my own current position in relation to the Grothendieck Programme, and also to that...
View ArticleAnswer by D.-C. Cisinski for Grothendieck's Homotopy Hypothesis -...
There are several ways to interpret the homotopy hypothesis.Strictly speaking, Grothendieck's homotopy hypothesis is not a theorem yet: Grothendieck stated it in a very precise way in the very first...
View ArticleAnswer by Todd Trimble for Grothendieck's Homotopy Hypothesis - Applications...
For me this result fits in a context of other results that give complete algebraic invariants for homotopy types. The broad program sometimes goes under the rubric Whitehead's algebraic homotopy...
View ArticleGrothendieck's Homotopy Hypothesis - Applications and Generalizations
Grothendieck's homotopy hypothesis, is, as the $n$lab states:Theorem:There is an equivalence of $(∞,1)$-categories $(\Pi⊣|−|): \mathbf{Top} \simeq \mathbf{\infty Grpd}$.What are the applications of...
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