[[Category theory MOC]]
# String diagram

**String diagrams** are a convenient notation for depicting 0-cells, 1-cells, and 2-cells in a [[Bicategory|bicategory]], and in particular, objects and morphisms in a [[monoidal category]].

![[Commutative_diagram_to_string_diagram.svg#invert]]

- a 0-cell is depicted as a face (in the case of a monoidal category there is only a single 0-cell)
- a 1-cell $f : X \to Y$ is depicted by a line with $X$ on the right and $Y$ on the left;
- a 2-cell $\beta : f \Rightarrow g : X\to Y$ is depicted as a node with $f$ coming out the bottom and $g$ coming out the top.

Horizontal composition is represented by horizontal juxtaposition, and vertical composition is represented by vertical juxtaposition.

## Bibliography

- 2011\. [[Sources/@baezPhysicsTopologyLogic2011|Physics, topology, logic and computation: A Rosetta stone]]
-  1996\. [[Sources/@streetCategoricalStructures1996|Categorical structures]]

#
---
#state/stub | #lang/en | #SemBr