Discussion Overview
The discussion revolves around the definition of identity arrows in category theory, specifically questioning whether the identity arrow can be considered a point rather than an arrow. Participants explore the implications of this definition and the terminology used in category theory.
Discussion Character
- Conceptual clarification, Debate/contested
Main Points Raised
- One participant suggests that the definition of the identity arrow id_A implies it is a point instead of an arrow, seeking clarification on this visualization.
- Another participant argues that while categories contain objects and arrows, the term "point" is not typically used in this context, emphasizing that arrows cannot be identified with objects.
- A third participant challenges the use of the term "relations" to describe arrows, noting that relations are generally subsets of Cartesian products, while arrows do not fit this definition in general.
- One participant introduces the terminology of objects and morphisms, suggesting that morphisms can be thought of as arrows and objects as boxes, akin to a flow chart.
Areas of Agreement / Disagreement
Participants express differing views on the terminology and conceptualization of identity arrows, with no consensus reached on whether id_A can be considered a point.
Contextual Notes
There are unresolved issues regarding the definitions and terminology used in category theory, particularly the distinction between arrows and objects, as well as the implications of identifying identity arrows with points.