adjunction
Meanings
伴随, 伴随函子.
Given a pair of categories \mathcal{C} and \mathcal{D}: an anti-parallel pair of functors F:\mathcal{C}\rightarrow \mathcal{D} and G:\mathcal{D}\rightarrow \mathcal{C} and a natural transformation \eta:\mbox{id}C \rightarrow GF called “unit” such that for any object A \in \mathcal{C}, for any object B \in \mathcal{D}, and for any morphism f:A\rightarrow GB, there is a unique morphism g:FA\rightarrow B such that Gg \circ \etaA = f. (Note: there is another natural transformation called “counit” as well but its existence may be derived by theorem.) The pair of functors express a similarity between the pair of categories which is weaker than that of an equivalence of categories.
Examples :
Related Words
connection noun
/kəˈnɛkʃən/
连接，联系。
"The connection between the two classrooms was established by installing a new phone line. "
通过安装一条新的电话线，两个教室之间建立了连接。
transformation noun
/ˌtɹæns.fə(ɹ)ˈmeɪ.ʃən/ /ˌtɹæns.fɔɹˈmeɪ.ʃən/
转变，转化，变革
"The transformation of the classroom from a noisy space to a quiet learning environment was remarkable. "
教室从喧闹的空间转变为安静的学习环境，这种转变非常显著。
