Topological functors and Cartesian-closed categories

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:

The construction is explained in more detail in this post (April 20th, 2023).


The full slides, with all animation steps; the shorter presentation, without them.


The full-length video; or the same one, in three parts:

  1. Cartesian-closed categories, and the Escardó-Lawson-Simpson construction (23:30)
  2. Topological functors (11:29)
  3. Building Cartesian-closed categories with topological functors (16:57)

Jean Goubault-Larrecq