Enriched accessible categories
1996 ◽
Vol 54
(3)
◽
pp. 489-501
◽
Keyword(s):
We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincide with the categories of ν-flat presheaves and also with the categories of ν-points of the categories of ν-presheaves. Moreover, the ν-locally finitely presentable categories are exactly the ν-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small ν-category Cis equivalent to the category of ν-finitely presentable ν-flat presheaves on C.
1973 ◽
Vol 8
(1)
◽
pp. 1-16
◽
Keyword(s):
1978 ◽
Vol 18
(3)
◽
pp. 357-371
◽
1975 ◽
Vol 12
(1)
◽
pp. 49-72
◽
1978 ◽
Vol 18
(1)
◽
pp. 125-135
1975 ◽
Vol 19
(2)
◽
pp. 180-195
◽
1970 ◽
Vol 3
(3)
◽
pp. 375-383
◽
1978 ◽
Vol 19
(3)
◽
pp. 445-456
◽
2016 ◽
Vol 10
(02)
◽
pp. 1750037