We describe a dictionary of geometry ⟷ algebra in Lagrangian topology. As a by-product, we obtain a tautological (in a particular sense which we explain) proof of a folklore conjecture (sometimes attributed to Kontsevich) claiming that the objects and structure of the derived Fukaya category can be represented through immersed Lagrangians. Our construction is based on certain Lagrangian cobordism categories endowed with a structure called surgery models.
"A Lagrangian pictionary." Kyoto J. Math. 61 (2) 399 - 493, June 2021. https://doi.org/10.1215/21562261-2021-0007X