Some Constructions in the Category of Topological Partial Actions

@misc{avila2026some,
  title = {{Some Constructions in the Category of Topological Partial Actions}},
  author = {Jesús Ávila and Fabián Molina},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00363},
  eprint = {2611.00363},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00363},
}

TY  - UNPB
TI  - Some Constructions in the Category of Topological Partial Actions
AU  - Jesús Ávila
AU  - Fabián Molina
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00363
UR  - https://arxiv.org/abs/2611.00363
AB  - 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.
ER  -