Category Archives: coreflection functor

The “tau topology” on the fundamental group

Posted on November 9, 2024 by Jeremy Brazas

In the multipart series on topologies on fundamental groups, we’ve discussed the fundamental group with the quotient topology: . This is defined as having the quotient topology with respect to the map , that identifies homotopic loops. Here, is the … Continue reading →

Posted in Category Theory, coreflection functor, Fundamental group, Quasitopological groups, quasitopological groups, quotient topology, reflection functor, topological fundamental group, Topological groups, Uncategorized | Tagged , , , , , , | 1 Comment

The locally path-connected coreflection (Part III)

Posted on December 6, 2014 by Jeremy Brazas

This post gives another look at the locally path-connected coreflection that I’ve found quite interesting and useful. For the previous posts see Part I and Part II. In this post, we’ll be motivated by the following two basic observations. Lemma … Continue reading →

Posted in Categorical Topology, Category Theory, coreflection functor, locally path connected | Tagged , , , , | 8 Comments