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The (Tetra) Category of Pseudocategories in an Additive 2-category with Kernels
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| datacite.subject.fos | Ciências Naturais::Ciências da Computação e da Informação | |
| datacite.subject.sdg | 03:Saúde de Qualidade | |
| datacite.subject.sdg | 07:Energias Renováveis e Acessíveis | |
| datacite.subject.sdg | 11:Cidades e Comunidades Sustentáveis | |
| dc.contributor.author | Martins-Ferreira, N. | |
| dc.date.accessioned | 2025-12-17T19:10:37Z | |
| dc.date.available | 2025-12-17T19:10:37Z | |
| dc.date.issued | 2008-08-21 | |
| dc.description.abstract | We describe the (tetra) category of pseudo-categories, pseudo-functors, natural transformations, pseudo-natural transformations, and modifications, as introduced in Martins-Ferreira (JHRS 1:47-78, 2006), internal to an additive 2-categorywith kernels, as formalized in Martins-Ferreira (Fields Inst Commun 43:387-410, 2004). In the context of a 2-Ab-category, we introduce the notion of a pseudomorphism and prove the equivalence of categories: PsCat(A) ̃PsMor(A) between pseudo-categories and pseudo-morphisms in an additive 2-category, A, with kernels- extending thus the well known equivalence Cat(Ab)̃Mor(Ab) between internal categories and morphisms of abelian groups. The leading example of an additive 2-category with kernels is Cat(Ab). In the case A=Cat(Ab) we obtain a description of the (tetra) category of internal pseudo-double categories in Ab, and particularize it to a description of the (tetra) category of internal bicategories in abelian groups. As expected, pseudo-natural transformations coincide with homotopies of 2-chain complexes (as in Bourn, J Pure Appl Algebra 66:229-249, 1990). | eng |
| dc.description.sponsorship | Acknowledgment - The author wishes to thank to Professor G. Janelidze for much appreciated help of various kinds. | |
| dc.identifier.citation | Martins-Ferreira, N. The (Tetra) Category of Pseudocategories in an Additive 2-category with Kernels. Appl Categor Struct 18, 309–342 (2010). https://doi.org/10.1007/s10485-008-9158-z. | |
| dc.identifier.doi | 10.1007/s10485-008-9158-z | |
| dc.identifier.eissn | 1572-9095 | |
| dc.identifier.issn | 0927-2852 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/15141 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Springer Nature | |
| dc.relation.hasversion | https://link.springer.com/article/10.1007/s10485-008-9158-z | |
| dc.relation.ispartof | Applied Categorical Structures | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Internal bicategory | |
| dc.subject | Internal pseudo-double category | |
| dc.subject | Pseudo-category | |
| dc.subject | Pseudo-functor | |
| dc.subject | Pseudo-natural transformation | |
| dc.subject | Modification | |
| dc.subject | 2-Ab-category | |
| dc.subject | Additive 2-category | |
| dc.subject | Pseudo-morphism | |
| dc.title | The (Tetra) Category of Pseudocategories in an Additive 2-category with Kernels | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 342 | |
| oaire.citation.startPage | 309 | |
| oaire.citation.title | Applied Categorical Structures | |
| oaire.citation.volume | 18 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Martins-Ferreira | |
| person.givenName | Nelson | |
| person.identifier | 485301 | |
| person.identifier.ciencia-id | B115-B65E-24AA | |
| person.identifier.orcid | 0000-0002-4199-7367 | |
| person.identifier.rid | N-1699-2013 | |
| person.identifier.scopus-author-id | 24598020700 | |
| relation.isAuthorOfPublication | 52406f6a-2c36-4e9a-9996-d3cc719d46bf | |
| relation.isAuthorOfPublication.latestForDiscovery | 52406f6a-2c36-4e9a-9996-d3cc719d46bf |
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- We describe the (tetra) category of pseudo-categories, pseudo-functors, natural transformations, pseudo-natural transformations, and modifications, as introduced in Martins-Ferreira (JHRS 1:47-78, 2006), internal to an additive 2-categorywith kernels, as formalized in Martins-Ferreira (Fields Inst Commun 43:387-410, 2004). In the context of a 2-Ab-category, we introduce the notion of a pseudomorphism and prove the equivalence of categories: PsCat(A) ̃PsMor(A) between pseudo-categories and pseudo-morphisms in an additive 2-category, A, with kernels- extending thus the well known equivalence Cat(Ab)̃Mor(Ab) between internal categories and morphisms of abelian groups. The leading example of an additive 2-category with kernels is Cat(Ab). In the case A=Cat(Ab) we obtain a description of the (tetra) category of internal pseudo-double categories in Ab, and particularize it to a description of the (tetra) category of internal bicategories in abelian groups. As expected, pseudo-natural transformations coincide with homotopies of 2-chain complexes (as in Bourn, J Pure Appl Algebra 66:229-249, 1990).
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