Limits of small functors

Brian J. Day; Stephen Lack

doi:10.1016/j.jpaa.2006.10.019

Limits of small functors

Brian J. Day, Stephen Lack^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

46 Citations (Scopus)

Abstract

For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K^op, V]. If K is large, its free completion under colimits is the V-category P K of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on P K.

Original language	English
Pages (from-to)	651-663
Number of pages	13
Journal	Journal of Pure and Applied Algebra
Volume	210
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2006.10.019
Publication status	Published - Sept 2007

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10.1016/j.jpaa.2006.10.019

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title = "Limits of small functors",

abstract = "For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [Kop, V]. If K is large, its free completion under colimits is the V-category P K of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on P K.",

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AU - Day, Brian J.

AU - Lack, Stephen

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AB - For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [Kop, V]. If K is large, its free completion under colimits is the V-category P K of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on P K.

UR - https://www.scopus.com/pages/publications/34247847979

U2 - 10.1016/j.jpaa.2006.10.019

DO - 10.1016/j.jpaa.2006.10.019

M3 - Article

AN - SCOPUS:34247847979

SN - 0022-4049

VL - 210

SP - 651

EP - 663

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -

Limits of small functors

Abstract

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