• informal definition from Categorical System Theory (1.3.4.1)
  • A algebraic theory $\mathbb{T}$ consists of:
    • a set $\mathbb{T}_{n}$ of $n$-ary operations for each $n \in \mathbb{N}$
    • a set of laws setting some composites of operations equal to others
• we can use it to organize the operations we can perform in wiring diagram
  • informal: A wiring diagram with operations from an algebraic theory $\mathbb{T}$ is a wiring diagram where operations from the theory $\mathbb{T}$ can be drawn in little green beads on the wires.
    • this is in contrast to a wiring diagram without any operation (pure wiring diagram)
  • ultimately, we want to say “wriring diagrams with operations from $\mathbb{T}$ are lenses in … cartesian category”
  • Lawvere theories is what we need