Abstract
We give here a very short account of the tools from (higher) category theory that will be used throughout this book. Some of these are not so standard outside of the category theory community, so that we shall record them for later reference. We first discuss higher categorical structures, and their use in categorical logics, through the notions of doctrines and theories. We then define monoidal and symmetric monoidal categories, and discuss their use in the theory of operads and properads. We finish by defining Grothendieck topologies, and giving a formal categorical setting for differential calculus, that will be used throughout the book.
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Paugam, F. (2014). A Categorical Toolbox. In: Towards the Mathematics of Quantum Field Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-04564-1_2
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