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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Online
ISSN
1898-9934
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Volume 23, Issue 1 (Mar 2015)

Issues

Categorical Pullbacks

Marco Riccardi
Published Online: 2015-03-31 | DOI: https://doi.org/10.2478/forma-2015-0001

Summary

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].

MSC: 18A30; 03B35

Keywords: category pullback; pullback lemma

MML: identifier: CAT 7; version: 8.1.03 5.29.1227

References

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About the article

Received: 2014-12-31

Published Online: 2015-03-31

Published in Print: 2015-03-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2015-0001.

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© Marco Riccardi. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. BY-SA 3.0

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