Abstract EN:

The main subject of this thesis is diagram rewriting.This is a generalisation to dimension~2 of word rewriting (in dimension~1). In a first time, we give the first convergent diagrammatic presentation of the PRO of linear maps in arbitrary field. Then we study the convergent diagrammatic presentation of matrix of isometries of RR^n. We focus especially on a rule similar to the Yang-Baxter equation, described by a certain map h. We use the confluence of criticalthe parametric diagrams, To study the algebraic properties of h, Finally, we present the ∑-diagrams, an alternative approach for calculation in bialgebras. We illustrate this approach with examples. The last two chapters have been already published: Diagram rewriting for orthogonal matrices: a study of critical peaks, avec Yves Lafont, Lecture Notes in Computer Science 5117, p. 232-245, 2008 Properties of co-operations: diagrammatic proofs, Mathematical Structures in Computer Science 22(6), p. 970-986, 2012.