Premonoidal category

Last updated Dec 2, 2024

Premonoidal categories are monoidal categories without the interchange law. Premonoidal categories can be defined via binoidal categories.

See also

• interchange law
  • premonoidal categories are monoidal categories without the interchange law
  • Binoidal and premonoidal categories
  • Premonoidal functor
  • unbiased premonoidal category
• effectful category
  • Freyd category
  • values and computation
  • copyable and discardable Freyd categories
  • coloring premonoidality
• monoid in a premonoidal category
  • monoid action on the runtime
• enrichment on a premonoidal category

• Feedback premonoidal category

References.

• Premonoidal Categories and a Graphical View of Programs (Jeffrey, 1997)
• Premonoidal Categories and Notions of Computation (Power, Robinson, 1997)
• Environments, continuation semantics and indexed categories (Power, Thielecke)
• Adjunctions whose counits are coequalizers and presentations of finitary enriched monads (Kelly, Power)
• Call-By-Push-Value, A Functional-Imperative Synthesis (Levy, 2004)
• String Diagrams for Premonoidal Categories (Román, Sobociński, 2023)