My equivalence of categories
Collection
| context | $F$ in ${\bf D}\longrightarrow{\bf C}$ |
| context | $G$ in ${\bf C}\longrightarrow{\bf D}$ |
| definiendum | $\langle\alpha,\beta\rangle$ in $F\simeq G$ |
| inclusion | $\alpha, \beta$ … my nice nats $\left(F,G\right)$ |
| inclusion | $\alpha,\beta$ … natural isomorphism |
Discussion
Elaboration
$\alpha$ in $FG\cong Id_{\bf C}$
$\beta$ in $Id_{\bf D}\cong GF$.
Note the two different symbols $\cong$ and $\simeq$. The first is about equivalences, the second about invertible gadgets.
Idea
This is like equivalence of categories, except the natural transformations are not just required to exist but must be concretely specified. As such, this is a subset of my nice nats.
Reference
Wikipedia: Equivalence of categories
Parents
Context
Subset of
Refinement of
Requirements
