|
12
2
|
Is there a standard construction of a classifying space $BC$ for a category $C$ which is enriched which takes into account the enrichment? This is of course vague... The simplest example I can think of arises when $C$ is enriched over abelian groups or $k$-modules for some commutative ring $k$. |
||
|
|
|
6
|
For a category enriched in topological spaces, the usual classifying space can be made to take into account the topology on morphisms. More generally this works for categories internal to top and is described here Segal "Classifying spaces and spectral sequences". Even more generally if you have a category enriched in a category C, and C has enough fiber products, then the nerve makes sense as a simplicial-C object. You can then try to construct the classifying space using a coend and a suitable cosimplicial object $\Delta \to C$ (In the case $C = Top$ this is the usual embedding). |
||||||||
|
