Things as categories
Many objects of study in mathematics may alternately be viewed as a special kind of category. Often this is related to oidification or Categorification.
Oidification
The following characterizes some structure as some single-object category, hence relate to oidification.
Vertical categorification
The following characterizes some structure as categories with subsingleton hom-sets, hence relate to vertical categorification
Free categories
Some structures can be studied by constructing a related “free” category (see also Representation)
- Free category (from a quiver)
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