To compensate for the lack of abstraction in the field of origami, in this paper, we propose a categorical description that can be introduced to map folding. Specifically, we use a particular expression to abstract the folding process of a map with logical matrices. When the folding operations are restricted to two certain kinds, the simple folds and the simple unfolds, we can define categories of partly folded states of the map as poset categories. The property of posets induces many general categorical concepts, such as (co)product, opposite category, direct system, and so on. We then introduce how these general concepts are specified in the proposed categories. These conceptions and specifications brought us the hope to solve and study the map folding with contemporary mathematical methods, such as the (co)homology. Furthermore, our categorical description can potentially be applied to a more generalized version of the map folding, the flat-folding.
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