Resourceful Traces for Commuting Processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908464381427712 |
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| author | Earnshaw, Matthew Nester, Chad Román, Mario |
| author_facet | Earnshaw, Matthew Nester, Chad Román, Mario |
| contents | We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for effectful categories (also known as generalised Freyd categories), a well-known algebraic structure in the semantics of side-effecting computation. Like the usual representation of traces as graphs, our notion of presentation gives rise to a graphical calculus for effectful categories. We use our presentations to give a construction of the commuting tensor product of free effectful categories, capturing the combination of systems in which the actions of each must commute with one another, while still permitting exchange of resources |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resourceful Traces for Commuting Processes Earnshaw, Matthew Nester, Chad Román, Mario Logic in Computer Science Category Theory We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for effectful categories (also known as generalised Freyd categories), a well-known algebraic structure in the semantics of side-effecting computation. Like the usual representation of traces as graphs, our notion of presentation gives rise to a graphical calculus for effectful categories. We use our presentations to give a construction of the commuting tensor product of free effectful categories, capturing the combination of systems in which the actions of each must commute with one another, while still permitting exchange of resources |
| title | Resourceful Traces for Commuting Processes |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2507.18246 |