  Category theory is now a common tool in the mathematician’s toolbox; that much is clear. It is also clear that category theory organizes and unifies much of mathematics. Contemporary mathematical fields would not be what they are without category theory, for instance algebraic topology, homological algebra, homotopy theory and homotopical algebra, representation theory, arithmetic geometry and algebraic geometry. (See for instance Mac Lane 1971, 1998 or Pedicchio &amp; Tholen 2004.) No one will deny these simple facts. Furthermore, vast portions of contemporary mathematics now rest on a different practice which rely, in large part, on the manipulation of new graphical notations, on the one hand, and on different levels of abstraction, on the other hand. It is not simply that category theory and the mathematical disciplines developed within that framework use commutative diagrams, although this in itself leads to some interesting philosophical explorations, as for instance in De Toffoli 2017, but category theorists have seen the need to develop systematic and formal graphical languages to express directly various forms of argumentations. (See, for instance, Joyal &amp; Street 1993; Joyal, Street &amp; Verity 1996; Fong &amp; Spivak 2019, Other Internet Resources.) Whereas since Bourbaki, mathematics was done “up to isomorphism”, in some cases, it is now done “up to equivalence” or up to “bi-equivalence” or even up to “n-equivalence”. (For an attempt at clarifying what these levels of abstraction mean, see Marquis 2014, Marquis 2016.)