String diagrams for closed categories
Wanted: a coherent graphical language for (non-compact) closed categories , ideally based on string diagrams.
Literature
String diagrams
- Baez & Stay, 2010: Physics, topology, logic, and computation: a Rosetta stone
(doi, arxiv)
- Introduces a “clasp and bubble” notation for closed categories
- In a compact closed category, deleting the clasps and bubbles recovers the usual graphical language
- Coecke et al, 2013: Lambek vs Lambek: Functorial vector space semantics and
string diagrams for Lambek calculus (doi, arxiv)
- Applies the “clasp-string calculus” to Lambek monoids
- Wijnholds, 2014, MSc thesis: Categorical foundations for extended
compositional distributional models of meaning (pdf)
- Identifies coherence problems with clasp-string language
- Advocates proof nets as alternative
Category theory, miscellaneous
- Jeffrey, 1998: Premonoidal categories and a graphical view of programs
(online )
- Graphical syntax for abstraction and recursion, among other things
- String diagrams not mentioned but are closely related—a great starting point!
Computer science