An Example Relating the Coarse and Weak Shape

Uglešić, Nikica

doi:10.1007/s00009-016-0784-7

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…It leads to a complete new paper. Another possible way might be, firstly, to find a suitable invariant of the J-shape (pro J -HTop) and, secondly, to prove that it is not an invariant of the coarse shape (pro * -HTop), which again asks for a transfinite construction on an uncountable well ordered index set (of an inverse system) as well as on (J, ≤) (see [25]).…”

Section: A J-shape Isomorphismmentioning

confidence: 99%

“…On that line, the most important has become a certain uniformization of the S-equivalence, called the S * -equivalence, which admits a categorical characterization, [23]. Moreover, it admits (genuine and different; [24][25]) generalizations to all topological spaces as well as to any abstract categorical framework [29], and all the well known shape invariants remain as the invariants of the both generalizations (in addition, [27]).…”

Section: Introductionmentioning

confidence: 99%

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Enriched Pro-Categories and Shapes

Uglešić¹

2022

Contemporary Mathematics

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Given a category C and a directed partially ordered set J, a certain category proJ-C on inverse systems in C is constructed such that the ordinary pro-category pro-C is the most special case of a singleton J ≡ {1}. Further, the known pro*-category pro*-C becomes proN-C. Moreover, given a pro-reflective category pair (C, D), the J-shape category ShJ(C, D) and the corresponding J-shape functor SJ are constructed which, in mentioned special cases, become the well known ones. Among several important properties, the continuity theorem for a J-shape category is established. It implies the “J-shape theory” is a genuine one such that the shape and the coarse shape theory are its very special instances.

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Section: A J-shape Isomorphismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enriched Pro-Categories and Shapes

Uglešić¹

2022

Contemporary Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…On that line, the most important has become a certain uniformization of the S-equivalence, called the S * -equivalence, which admits a categorical characterization, [25]. Moreover, it admits (genuine and different; [31], [33]) generalizations to all topological spaces as well as to any abstract categorical framework ( [19], [34], [36]]), and all the well known shape invariants remain as the invariants of the both generalizations (in addition, [18] and [29]).…”

Section: Introductionmentioning

confidence: 99%

Enriched pro-categories and shapes

Uglešić¹

2019

Preprint

Self Cite

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Given a category C and a directed partially ordered set J, a certain category pro J -C on inverse systems in C is constructed such that the ordinary pro-category pro-C is the most special case of a singleton J ≡{1}. Further, the known pro * -category pro * -C becomes pro N -C. Moreover, given a pro-reflective category pair (C, D), the J-shape category Sh J (C,D) and the corresponding J-shape functor S J are constructed which, in mentioned special cases, become the well known ones. Among several important properties, the continuity theorem for a J-shape category is established. It implies the "J-shape theory" is a genuine one such that the shape and the coarse shape theory are its very special examples.

show abstract

An Example Relating the Coarse and Weak Shape

Cited by 2 publications

References 5 publications

Enriched Pro-Categories and Shapes

Enriched Pro-Categories and Shapes

Enriched pro-categories and shapes

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