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

Parents

Context

Subset of

Refinement of

Requirements

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