Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Abstraction: Accessible introduction to applied category theory via seven concrete examples

Key points:

• Seven "sketches" each pair a real-world application (databases, electric circuits, dynamical systems, etc.) with a categorical structure (adjoint functors, enriched categories, toposes, etc.)
• Designed as a gentle, quick tour requiring no prior category theory knowledge
• Authored by Brendan Fong and David Spivak (MIT, 2018); widely used as introductory text for applied category theory
• Emphasizes compositionality as the organizing principle: how complex systems are built from simpler interacting parts
• Covers monoidal categories, decorated cospans, and Lawvere metric spaces among other structures
• Part of a broader movement connecting category theory to engineering, computer science, and the sciences

Connections: Brendan Fong · David Spivak · Category Theory · Applied Category Theory · Compositionality

Source: https://arxiv.org/abs/1803.05316