An alternative Gospel of structure: order, composition, processes
It provides an incremental introduction to foundational structures for researchers in linguistics, physics, and knowledge representation.
The paper surveys basic mathematical structures like orders and monoidal categories, which are argued to be more primitive than traditional ones, and introduces their applications in linguistics, physics, and knowledge representation.
We survey some basic mathematical structures, which arguably are more primitive than the structures taught at school. These structures are orders, with or without composition, and (symmetric) monoidal categories. We list several `real life' incarnations of each of these. This paper also serves as an introduction to these structures and their current and potentially future uses in linguistics, physics and knowledge representation.