Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

I will first explain a relative version of functorial field theories and give a classification thereof. This will allow to constructs simple examples using dualizability results. The main tool is that of a factorization algebra and the pictures which appear strongly resemble string diagrams and correspond to algebraic manipulations. Moreover, I will compare to previous results by Douglas-Schommer-Pries-Snyder and Brochier-Jordan-Snyder on Turaev-Viro and Reshetikin-Turaev theories. The final goal is to showcase low-dimensional field theories which are “relative” to their observables.