DC Field | Value | Language |
---|---|---|
dc.contributor.author | Femić, Bojana | en_US |
dc.date.accessioned | 2023-11-23T14:31:28Z | - |
dc.date.available | 2023-11-23T14:31:28Z | - |
dc.date.issued | 2023 | - |
dc.identifier.issn | 1201-561X | - |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/5220 | - |
dc.description.abstract | We introduce a candidate for the inner hom for the category of double categories and lax double functors, and characterize a lax double functor into it obtaining a lax double quasi-functor. The latter consists of a pair of lax double functors with four 2-cells resembling distributive laws. We extend this characterization to a double category isomorphism. We show that instead of a Gray monoidal product we obtain a product that in a sense strictifies lax double quasi-functors. We explain why laxity of double functors hinders our candidate for the inner hom from making the category of double categories and lax double functors a closed and enriched category over 2-categories (or double categories). We prove a bifunctor theorem by which certain type of lax double quasi-functors give rise to lax double functors on the Cartesian product. We extend this theorem to a double functor between double categories and show how it restricts to a double equivalence. The (un)currying double functors are studied. We prove that a lax double functor from the trivial double category is a monad in the codomain double category, and show that our above double functor recovers the specification in that double category of the composition natural transformation on the monad functor. | en_US |
dc.publisher | Mount Allison University | en_US |
dc.relation.ispartof | Theory and Applications of Categories | en_US |
dc.subject | bicategories | double categories | Gray monoidal product | en_US |
dc.title | BIFUNCTOR THEOREM AND STRICTIFICATION TENSOR PRODUCT FOR DOUBLE CATEGORIES WITH LAX DOUBLE FUNCTORS | en_US |
dc.type | Article | en_US |
dc.identifier.scopus | 2-s2.0-85174073763 | - |
dc.identifier.url | http://www.tac.mta.ca/tac/volumes/39/29/39-29.pdf | - |
dc.contributor.affiliation | Mathematics | en_US |
dc.contributor.affiliation | Mathematical Institute of the Serbian Academy of Sciences and Arts | - |
dc.relation.firstpage | 824 | - |
dc.relation.lastpage | 874 | - |
dc.relation.volume | 39 | - |
dc.description.rank | ~M23 | - |
item.grantfulltext | none | - |
item.cerifentitytype | Publications | - |
item.fulltext | No Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | Article | - |
crisitem.author.dept | Mathematical Institute of the Serbian Academy of Sciences and Arts | - |
crisitem.author.orcid | 0000-0002-5767-1708 | - |
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