This is a talk I gave at the seminar on categorical topology at Benemérita Universidad Autónoma de Puebla, Puebla, México, on May 24th, 2023 (or rather, for which I recorded a series of videos to be played there), on invitation from Frédéric Mynard.
The category Top of topological spaces and continuous maps is not Cartesian-closed. Martín Escardó, Jimmie Lawson and Alex Simpson gave a wonderful construction of many Cartesian-closed, coreflective full subcategories of Top. I will show that this construction generalizes beyond Top to topological functors. In a sense, this whole talk is an excuse to give an introduction to the wonderful notion of topological functors.
This is based on the following paper:
- Jean Goubault-Larrecq. Exponentiable streams and prestreams. Applied Categorical Structures 22, pages 515–549, 2014. The published version, available from Springer Link, contains two mistakes, which are repaired in the HAL report.
The construction is explained in more detail in this post (April 20th, 2023).
The full-length video; or the same one, in three parts:
- Cartesian-closed categories, and the Escardó-Lawson-Simpson construction (23:30)
- Topological functors (11:29)
- Building Cartesian-closed categories with topological functors (16:57)