This paper is towards the study of L-fuzzy automata from the categorical point of view, where L is a complete residuated lattice. We introduce a functor having both the left/right adjoint from the category of L-fuzzy Σ-semiautomata $\mathbf{LFSA}(\mathrm{\Sigma })$ to the category LFTCRL(Σ), a category of complete residuated lattices corresponding to L-fuzzy Σ-semiautomata. The L-fuzzy response map of an L-fuzzy automaton leads us to provide a characterization of an L-fuzzy regular language. Interestingly, we show that the category $\mathbf{LFSA}(\mathrm{\Sigma })$ is a category of ${\mathcal{T}}_1$-coalgebras/$({\mathcal{T}}_2,{\mathcal{T}}_3)$-dialgebras. Moreover, we establish a relationship between the category of ${\mathcal{T}}_1$-coalgebras and the category of $({\mathcal{T}}_2,{\mathcal{T}}_3)$-dialgebras.

本文是从分类的角度研究L-模糊自动机，其中L是一个完全剩余格。我们从L -fuzzy Σ-semiautomata的范畴中引入了一个同时具有左/右伴随的函子$\mathbf{LFSA}(\mathrm{\Sigma })$到类别LFTCRL (Σ)，对应于L-模糊 Σ-半自动机的完整剩余格的类别。L -模糊自动机的L -模糊响应图引导我们提供L -模糊正则语言的特征。有趣的是，我们证明了类别$\mathbf{LFSA}(\mathrm{\Sigma })$ 是一类 ${\mathcal{吨}}_1$- 代数/$({\mathcal{吨}}_2,{\mathcal{吨}}_3)$- 代数。此外，我们建立了类别之间的关系${\mathcal{吨}}_1$- 代数和范畴 $({\mathcal{吨}}_2,{\mathcal{吨}}_3)$- 代数。