pilin kiwen pi ma Katekoli lon toki pona

ma Katekoli $\mathcal{C}$ li alasa e ni:

• kulupu $\mathrm{ob}(\mathcal{C})$ pi ijo ale
• kulupu $\mathcal{C}(A,B)$ pi nasin ale tan ijo $A$ tawa ijo $B$

(nasin $f$ li tan ijo $A$ tawa ijo $B$ la, sitelen $f:A\to B$ li lon)

• nasin pini ${\mathrm{id}}_A:A\to A$ pi ijo $A$
• nasin suli $g\circ f:A\to C$ pi nasin $f:A\to B$ pi nasin $g:B\to C$

ma Katekoli $\mathcal{C}$ li jo e lawa ni:

• nasin $f$ li tan ijo $A$ tawa ijo $B$ la, nasin suli ${\mathrm{id}}_B\circ f$ en nasin suli $f\circ {\mathrm{id}}_A$ li nasin sama $f$.
• nasin tu wan $A\stackrel{f}{\to }B\stackrel{g}{\to }C\stackrel{h}{\to }D$ li lon la, nasin suli $h\circ (g\circ f)$ pi nasin $g\circ f$ pi nasin $h$ li nasin $(h\circ g)\circ f$ pi nasin $f$ pi nasin sama $h\circ g$.