# exponential object

## English

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### Noun

exponential object (plural exponential objects)

1. (category theory) A categorical object which generalizes its interpretation in category Set; namely, as a function set[1]. An exponential may be introduced through the "currying" inference rule[2] ${f : C \times A \rightarrow B \over \lambda_f : C \rightarrow B^A}$ and eliminated through the "function application" ("eval") rule[2] $\epsilon_{{}_{A, B}} : B^A \times A \rightarrow B$.

### References

1. ^ ncatlab.org's article on function set (Revision 237)
2. Jeltsch, Wolfgang (2012). An Introduction to Category Theory and Categorical Logic, slide 20.