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Categorical Pullbacks

100%

Riccardi M.

Formalized Mathematics

2015

tom 23

nr 1

1-14

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].

Coproduct of Crossed A-Modules of R-Algebroids

64%

Avcıoglu O., Akça I. I.

Topological Algebra and its Applications

2017

tom 5

nr 1

37-48

In this study we construct, in the category XAlg(R) / A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (μ : M → A) and N = (ɳ : N → A) of R-algebroids in two different ways: Firstly we construct the coproduct M ᴼ* N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M ᴼ⋉ N by using the semidirect product M ⋉ N of M and N via μ. Finally we construct an isomorphism betweenM ᴼ* N and M ᴼ⋉ N.

Ograniczanie wyników

1 Formalized Mathematics

1 Topological Algebra and its Applications

1 Akça I. I.

1 Avcıoglu O.

1 Riccardi M.

1 2017

1 2015

Wyniki wyszukiwania

Categorical Pullbacks

Coproduct of Crossed A-Modules of R-Algebroids