We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces s of practical interest.
Antoine, J.-P., Lambert, D., & Trapani, C. (2011). Partial inner product spaces: Some categorical aspects. Advances in Mathematical Physics, 2011, Article ID 957592 (22 pages). https://doi.org/10.1155/2011/957592 (Original work published 2011)