pilin kiwen pi ma Katekoli lon toki pona

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

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

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

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

ma Katekoli $\mathscr{C}$ 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 $A \xrightarrow{f} B \xrightarrow{g} C \xrightarrow{h} D$ 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 $h \circ g$.