exponential object

English - English

Definition of exponential object in English English dictionary

Given objects Y and Z, the exponential object Z^Y is uniquely defined by the following universal property: for any object X with arrow f: X \times Y \rightarrow Z, there can always be constructed an arrow \lambda f: X \rightarrow Z^Y which induces an arrow \lambda f \times \hbox{id}_Y = g , g: X \times Y \rightarrow Z^Y \times Y which is unique in satisfying h \circ g = f where h: Z^Y \times Y \rightarrow Z

In the Sets category, given sets A and B with A = \{a, b, c, ..., z\} then if B_a = \{a\} \times B , B_b = \{b\} \times B , ..., B_z = \{z\} \times B , then the product of A and B is A \times B = B_a \cup B_b \cup ... \cup B_z and the exponential is B^A = B_a \times B_b \times ... \times B_z .

Hyphenation

ex·po·nen·tial ob·ject

Turkish pronunciation

ekspōnenşıl ıbcekt

Pronunciation

/ˌekspōˈnensʜəl əbˈʤekt/ /ˌɛkspoʊˈnɛnʃəl əbˈʤɛkt/