All Questions
Tagged with enriched-category-theory simplicial-categories
5
questions
2
votes
0
answers
118
views
Are homotopy colimits strict?
Let's say we are working with a fibrant simplicially enriched category $\mathbf{B}$ that has all limits and all homotopy limits, and let $\mathbf{A}$ be a full subcategory that is closed under weak ...
1
vote
0
answers
64
views
Tensored and cotensored simplicial comma category
To transfer a tensored and cotensored simplicially enriched structure from a category $\mathcal{C}$ to $(\mathcal{C}\downarrow Z)$, we define $(X\to Z)\otimes K$ by the composite $(X\otimes K \to X \...
6
votes
0
answers
77
views
Is composition in a simplicially enriched category always determined by a compatible simplicial tensoring (if such exists)?
Let $C$ be a simplicially enriched category, i.e., there are
a collection of objects $ob C$,
a simplicial set $map_C(X,Y)$ for $X,Y \in ob C$,
composition maps $map_C(Y,Z) \times map_C(X,Y) \to map (...
4
votes
0
answers
574
views
How to compute (co)limits of enriched categories?
I've asked this question on math.stackexchange some time ago (https://math.stackexchange.com/questions/1380176/how-to-compute-colimits-of-enriched-categories) and I received no complete answers, so I'...
0
votes
1
answer
285
views
equivalence in simplicial category
Let $(\mathcal{C},W)$ be a category with weak equivalences. One can build from $(\mathcal{C},W)$ its hammock localization $L^{H}(\mathcal{C},W)$ which is a simplicial category $\textit{ie}$ a category ...