恒等写像
word(s,s)! …【\(\text{id} _{ {\sf X} }\)】\(\text{id}.\)【\(\text{id} _{ X } = [ x \in X \mid x ]\)】
\(\text{id0}\)【\(\text{id} _{ X } \in X \stackrel{\rm IS}\to X\)】\(\blacktriangleleft\)
\(|\text{id}\)【\(R \in \text{Rel} \Longrightarrow R | _{ X } = R \circ \text{id} _{ X }\)】\(\blacktriangleleft\)
\({\stackrel{\rm I}\to}{.}{.}\)【\(X \stackrel{\rm I}\to Y = \{ f \in X \to Y \mid f ^\leftrightarrow \circ f = \text{id} _{ X } \}\)】\(\blacktriangleleft\)
\({\stackrel{\rm S}\to}{.}{.}\)【\(X \stackrel{\rm S}\to Y = \{ f \in X \to Y \mid f \circ f ^\leftrightarrow = \text{id} _{ Y } \}\)】\(\blacktriangleleft\)
to:I.. / d. < %0 , sw. と to:S.. / d. < %0 , sw. もOK
濃度
word(ss,p) … \(\stackrel{\#}\le\) \(\stackrel{\#}=\)\(\stackrel{\#}\le.\)【\(X \stackrel{\#}\le Y \Longleftrightarrow X \stackrel{\rm I}\to Y \neq \emptyset\)】
\(\stackrel{\#}=.\)【\(X \stackrel{\#}= Y \Longleftrightarrow X \stackrel{\rm IS}\to Y \neq \emptyset\)】
\({\stackrel{\#}=}自 \)【\(X \stackrel{\#}= X\)】\(\blacktriangleleft\)
\({\stackrel{\#}=}対\)【\(X \stackrel{\#}= Y \Longrightarrow Y \stackrel{\#}= X\)】
\({\stackrel{\#}=}推\)【\(X \stackrel{\#}= Y \stackrel{\#}= Z \Longrightarrow X \stackrel{\#}= Z\)】\(\blacktriangleleft\)
\({\stackrel{\#}<}推\)【\(X \stackrel{\#}\le Y \stackrel{\#}\le Z \Longrightarrow X \stackrel{\#}\le Z\)】\(\blacktriangleleft\)