The eventual image of an endomorphism is the intersection of the images of its iterates?. This makes sense in many different categories.
On the category of finite sets, the operation assigning to each endomorphism its eventual image is a dinatural transformation.
This example can also be viewed in terms of the trace of FinSet, defined as . Indeed, the value of under the canonical map is the same as that of the restriction to its eventual image, which is a permutation, and the value may be regarded as the conjugacy class of that permutation.
Tom Leinster, The eventual image (blog post)
Tom Leinster, The eventual image, part 2 (blog post)
Last revised on June 17, 2016 at 10:34:22. See the history of this page for a list of all contributions to it.