The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property and the Pullback Lemma is formalized [15]. In the last part of the article we formalize the pullback of functors [14] and it is also shown that it is not possible to write an equivalent definition in the context of the previous Mizar formalization of category theory [8].
@article{bwmeta1.element.doi-10_2478_forma-2015-0001,
author = {Marco Riccardi},
title = {Categorical Pullbacks},
journal = {Formalized Mathematics},
volume = {23},
year = {2015},
pages = {1-14},
zbl = {1317.18006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2015-0001}
}
Marco Riccardi. Categorical Pullbacks. Formalized Mathematics, Tome 23 (2015) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2015-0001/
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