Some Constructions in the Category of Topological Partial Actions

Jesús Ávila; Fabián Molina

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arXiv · 2611.00363

Some Constructions in the Category of Topological Partial Actions

Jesús Ávila·Fabián Molina

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Abstract

We present some theoretical aspects of the categories of global and partial group actions of topological groups on topological spaces, denoted by G-ActTop and G-pActTop, respectively. We construct topological partial actions on products and disjoint unions of topological spaces, and G-pinvariant subspaces. Furthermore, we provide an adequate definition of congruence (G-pcongruence), which enables the construction of quotient objects in the category of topological partial actions. In addition, we associate a special G-pcongruence to each pair of strong G-pmorphisms. Then, we study products, co-products, equalizers, co-equalizers, pullbacks, and pushouts in the category G-pActTop. We find that the category of topological partial actions is finitely complete and contains a co-complete subcategory. Finally, we show that the relationship between a topological partial action and its enveloping action is functorial. As a consequence, we obtain that the categorical product in G-ActTop coincides with the categorical product in G-pActTop. Moreover, the envelope of a co-product in G-pActTop is given by the co-product of the respective envelopes.

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Jesús Ávila, Fabián Molina. 2026-10-30. Some Constructions in the Category of Topological Partial Actions. https://arxiv.org/abs/2611.00363

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