Questions tagged [simplicial-categories]
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Defining homotopy via endofunctors of a simplicial category
$\newcommand\sSets{\text{sSets}}\newcommand\sing{\text{sing}}\DeclareMathOperator\Hom{Hom}\newcommand\Top{\text{Top}}$I am looking for a reference describing the notions of homotopy and ...
- 317
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Morphisms of hammocks in the simplicial localization
Let $\mathcal{C}$ be a category together with a wide subcategory $\mathcal{W} \subset \mathcal{C}$.
In Calculating Simplicial Localizations by Dwyer and Kan, a morphism of hammocks is defined to ...
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Modern proofs for simplicial localizations
I know that the references usually regarded as standard for simplicial localizations are the Dwyer and Kan's three articles from the 80's. I would be interested in a more modern approach to the ...
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Is the simplicial nerve a localization?
Given a simplicial category $\mathcal{C}_{\ast}$ (if necessary, you may assume it's fibrant), denote as $\mathcal{C}$ its underlying ordinary category, and as $\mathcal{W}$ the class of all ...
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When is a right lifting property closed under pushouts?
A class of morphisms defined by a right Quillen lifting property (weak orthogonality)
is always closed under pullbacks (limits); under what assumptions will it be closed under pushouts (colimits)? In ...
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Homotopy coherent colimits in chain complexes
In remark 1.2.6.2 (HTT), Lurie states that
Another possible approach to the problem of homotopy
coherence is to restrict our attention to simplicial (or topological) categories
C in which every ...
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Defining homotopy via the “doubling” endofunctor of a simplicial category
I am looking for a reference explicitly defining simplicial homotopy
in terms of endofunctors of $\Delta$, and developing homotopy theory in this terms.
The following is a particular question.
Is it ...
- 317