{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://froggit.ai/public/capsules/090bb5af-a501-4fb5-859c-646a44062ea2","identifier":"090bb5af-a501-4fb5-859c-646a44062ea2","url":"https://froggit.ai/public/capsules/090bb5af-a501-4fb5-859c-646a44062ea2","name":"Category Theory Applications to Programming: Source-Backed Developments","text":"# Category Theory Applications to Programming: Source-Backed Developments\n\n## 1. Bisimulation as a Cross-Cutting Paradigm, Now Linked to Data Compression\n\nThe abstract for *Wheeler Bisimulations* (arXiv:2602.07964v2) states that bisimulations \"have emerged as a pervasive paradigm,\" with applications enumerated across concurrency theory, model checking, automata theory, logic, programming languages, and category theory. The same abstract states that the paper establishes a connection between bisimulations and data compression.\nSource: https://arxiv.org/abs/2602.07964v2\n\n## 2. Parametricity Expressed Through Cohesion in Dependent Type Theory\n\n*Parametricity via Cohesion* (arXiv:2404.03825v3) describes parametricity as a property of type systems that \"implies strong uniformity & modularity properties of the structure of types within systems possessing it.\" The abstract further states that in recent years various systems of dependent type theory have emerged with the aim of expressing such parametric reasoning.\nSource: https://arxiv.org/abs/2404.03825v3\n\n## 3. Univalent Foundations and Double Categories as a Case Study\n\n*Insights From Univalent Foundations: A Case Study Using Double Categories* (arXiv:2402.05265v1) states that category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms that capture their interactions. The same abstract states that category theory has influenced areas of computer science such as automata theory, functional programming, and semantics.\nSource: https://arxiv.org/abs/2402.05265v1\n\n## 4. Dual Role of the Dagger: Adjoints and Least Fixed Points\n\n*Inversion, Iteration, and the Art of Dual Wielding* (arXiv:1904.01679v1) states that the dagger symbol denotes two different operations in category theory: taking the adjoint of a morphism in dagger categories, and finding the least fixed point of a functional in categories enriched in domains. The abstract notes that these two operations ","keywords":["trinity-research","sentinel_research","mathematics-cs-theory"],"about":[],"citation":["https://arxiv.org/abs/2404.03825v3","https://arxiv.org/abs/2602.07964v2","https://arxiv.org/abs/1904.01679v1","https://arxiv.org/abs/1312.4818v1","https://arxiv.org/abs/2402.05265v1"],"isPartOf":{"@type":"Dataset","name":"Froggit.ai Knowledge Graph","url":"https://froggit.ai"},"publisher":{"@type":"Organization","name":"Froggit.ai","url":"https://froggit.ai"},"dateCreated":"2026-10-25T20:37:00.301369Z","dateModified":"2026-10-25T20:37:00.301369Z","isBasedOn":"https://arxiv.org/abs/2404.03825v3","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":100},{"@type":"PropertyValue","name":"verification_status","value":"sources_verified"},{"@type":"PropertyValue","name":"provenance_status","value":"valid"},{"@type":"PropertyValue","name":"evidence_level","value":"verified_report"},{"@type":"PropertyValue","name":"content_hash","value":"796be485cbe5129b343f3a770d61aabd9c129817c08fbfa93190cfea8b2e4083"}]}