<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper has two parts. In the first part we present a case in which we can calculate in a simple way the product of two inverse systems as object in a pro-category of a category with directed products, without counting systems at the same set of indices. In the second part, which is related to some papers of Keesling [<xref ref-type="bibr" rid="j_auom-2019-0024_ref_004_w2aab3b7b8b1b6b1ab1ab4Aa">4</xref>], Kodama [<xref ref-type="bibr" rid="j_auom-2019-0024_ref_005_w2aab3b7b8b1b6b1ab1ab5Aa">5</xref>], Mardešić [<xref ref-type="bibr" rid="j_auom-2019-0024_ref_007_w2aab3b7b8b1b6b1ab1ab7Aa">7</xref>], and Dydak-Mardešić [<xref ref-type="bibr" rid="j_auom-2019-0024_ref_010_w2aab3b7b8b1b6b1ab1ac10Aa">10</xref>], we give a sufficient condition by which a directed product of a category 𝒯 is transformed by a shape functor <italic>S</italic> : 𝒯 → <italic>Sh</italic>(𝒯, 𝒫) into a directed product. This theorem is applied to the toplogical shape category Sh(Top) where some examples are obtained.</p></abstract>

This paper has two parts. In the first part we present a case in which we can calculate in a simple way the product of two inverse systems as object in a pro-category of a category with directed products, without counting systems at the same set of indices. In the second part, which is related to some papers of Keesling [4], Kodama [5], Mardešić [7], and Dydak-Mardešić [10], we give a sufficient condition by which a directed product of a category 𝒯 is transformed by a shape functor S : 𝒯 → Sh(𝒯, 𝒫) into a directed product. This theorem is applied to the toplogical shape category Sh(Top) where some examples are obtained.

On some products in pro-categories and shape categories

Faculty of Mathematics “Al.I.Cuza” University

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On some products in pro-categories and shape categories"}

This paper has two parts. In the first part we present a case in which we can calculate in a simple way the product of two inverse systems as object in a...

On some products in pro-categories and shape categories

Published Online: Sep 26, 2019

Page range: 139 - 151

Received: Oct 29, 2018

Accepted: Nov 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0024

Keywords
Products in a category, inverse systems, pro-category, shape category

© 2019 I. Pop, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On some products in pro-categories and shape categories

Published Online: Sep 26, 2019

Page range: 139 - 151

Received: Oct 29, 2018

Accepted: Nov 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0024

KeywordsProducts in a category, inverse systems, pro-category, shape category

© 2019 I. Pop, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Products in a category, inverse systems, pro-category, shape category