In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].
@article{bwmeta1.element.doi-10_1515_forma-2015-0028,
author = {Marco Riccardi},
title = {Exponential Objects},
journal = {Formalized Mathematics},
volume = {23},
year = {2015},
pages = {351-369},
zbl = {1334.18001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_forma-2015-0028}
}
Marco Riccardi. Exponential Objects. Formalized Mathematics, Tome 23 (2015) pp. 351-369. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_forma-2015-0028/
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