In this paper, we propose a formalism for knowledge manipulation, based on conceptual graphs, which is supported by category theory and which can be the basis for the development of knowledge-based systems. The model we propose is an extension of the model based on conceptual graphs. In this model, the application of an inference rule between logical formulas represented by two conceptual graphs is reduced to the identification of an arrow in a category. To this end, we introduce several new notions such as: the category of conceptual graphs, the category of classes of conceptual graphs, the conceptual category of a model and the conceptual category of inference of a model.
