Last modified date: <%+ tp.file.last_modified_date() %>
- Tags
- Refs:
-
Links:
- spectral category
Enriched category
V-enriched
Last modified date: <%+ tp.file.last_modified_date() %>
Alternatively: take subcategory of fibrant objects, observe enrichment over chain complexes, apply Dold-Kan to get a simplicial enrichment, then take the homotopy coherent nerve or simplicial nerve.
Finite tensor category : looks like \({}_{H}{\mathsf{Mod}}\), Unsorted/enriched category over vector spaces, Monoidal category, coherent associativity via pentagon axiom, triangle axiom.
What does it mean for a category to be enriched?
Note that the category of Unsorted/enriched category in topological spaces. There is a topological space \begin{align*} M\coloneqq\mathop{\mathrm{Maps}}(X, K({\mathbf{G}}_m, n)) \end{align*} where the homotopy groups are \begin{align*} \pi_i M = \begin{cases} H^{n-i}_{\text{ét}}(X, {\mathbf{G}}_m) & 0\leq i \leq n \\ 0 & \text{else} \end{cases} .\end{align*}
2-category : a category enriched in small categories, so hom sets are categories and compositions form bifunctors.