Timeline for What is the right notion of a functor from an internal topological category to a topologically enriched category?
Current License: CC BY-SA 4.0
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| May 27, 2022 at 10:30 | comment | added | Mike Shulman | But actually, you don't really even need any of that for the bare definition, which works perfectly well for functors from an internal category to any indexed category (i.e. fibration) over Top, and any category with pullbacks is self-indexed (i.e. has a codomain fibration). | |
| May 27, 2022 at 10:28 | comment | added | Mike Shulman | Note that your category of topological spaces has to be very convenient to be locally internal over itself. The naive approach requires a locally cartesian closed category, which excludes the standard examples like compactly generated spaces. There are locally cartesian closed examples, such as subsequential spaces or convergence spaces, but also May and Sigurdsson discovered that you can get the relevant parts of local cartesian closure if you take the base spaces to be compactly generated but only require those in the fibers to be k-spaces (no weak Hausdorff condition). | |
| May 27, 2022 at 8:08 | vote | accept | Niall Taggart | ||
| May 25, 2022 at 23:50 | history | answered | Mike Shulman | CC BY-SA 4.0 |