Are the following statements four ways of saying exactly the same thing?
1. (Stating that) a category C and its opposite category C* (its dual) are equivalent.
2. C and C* are thus self-dual (by virtue of being opposite categories to each other, and being equivalent).
3. C and C* are thus dually equivalent.
4. C and C* thus constitute a "duality of categories".
In short, are "equivalence of opposite categories", "self-dual categories", and "dually equivalent categories", synonymous expressions ?
2026-04-06 00:17:29.1775434649