In this paper, we develop a mathematically conceived semiotic theory. This project seems essential for a future computational creativity science since the outcome of the process of creativity must add new signs to given semiotic contexts. The mathematical framework is built upon categories of functors, in particular linearized categories deduced from path categories of digraphs and the Gabriel–Zisman calculus of fractions. Semantics in this approach is extended to a number of “global” constructions enabled by the Yoneda Lemma, including cohomological constructions. This approach concludes with a short discussion of classes of creativity with respect to the proposed functorial semiotics.

在本文中，我们开发了一种数学概念的符号学理论。这个项目对于未来的计算创意科学来说似乎至关重要，因为创意过程的结果必须为给定的符号环境添加新的标志。数学框架建立在函子的类别上，尤其是根据图的路径类别和分数的Gabriel-Zisman微积分推导的线性化类别。这种方法的语义学扩展到了由Yoneda Lemma支持的许多“全局”结构，包括同调结构。这种方法以关于拟议的功能符号学的创造力类别的简短讨论作为结束。