Nearly locally presentable categories
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Here1, in the remark $2.3 (1)$ how from the fact that ${cal K}(A,-)$ does not preserve coproducts it follows that ${cal K}(A,-)$ sends special $lambda$-directed colimits to $lambda$-directed colimits and not to special $lambda$-directed ones?
1
Leonid Positselski, Jiří Rosický: Nearly locally presentable categories,
Theory and Appl. of Categories 33 (2018), #10, p.253-264;
http://www.tac.mta.ca/tac/volumes/33/10/33-10abs.html https://arxiv.org/abs/1710.10476
category-theory functors representable-functor hom-functor locally-presentable-categories
edited 3 hours ago
Martin Sleziak
44.3k7115266
asked 20 hours ago
user122424
1,0641616
add a comment |
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1
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Here1, in the remark $2.3 (1)$ how from the fact that ${cal K}(A,-)$ does not preserve coproducts it follows that ${cal K}(A,-)$ sends special $lambda$-directed colimits to $lambda$-directed colimits and not to special $lambda$-directed ones?
1
Leonid Positselski, Jiří Rosický: Nearly locally presentable categories,
Theory and Appl. of Categories 33 (2018), #10, p.253-264;
http://www.tac.mta.ca/tac/volumes/33/10/33-10abs.html https://arxiv.org/abs/1710.10476
category-theory functors representable-functor hom-functor locally-presentable-categories
edited 3 hours ago
Martin Sleziak
44.3k7115266
asked 20 hours ago
user122424
1,0641616
To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Here1, in the remark $2.3 (1)$ how from the fact that ${cal K}(A,-)$ does not preserve coproducts it follows that ${cal K}(A,-)$ sends special $lambda$-directed colimits to $lambda$-directed colimits and not to special $lambda$-directed ones?
1
Leonid Positselski, Jiří Rosický: Nearly locally presentable categories,
Theory and Appl. of Categories 33 (2018), #10, p.253-264;
http://www.tac.mta.ca/tac/volumes/33/10/33-10abs.html https://arxiv.org/abs/1710.10476
category-theory functors representable-functor hom-functor locally-presentable-categories
edited 3 hours ago
Martin Sleziak
44.3k7115266
asked 20 hours ago
user122424
1,0641616
Here1, in the remark $2.3 (1)$ how from the fact that ${cal K}(A,-)$ does not preserve coproducts it follows that ${cal K}(A,-)$ sends special $lambda$-directed colimits to $lambda$-directed colimits and not to special $lambda$-directed ones?
1
Leonid Positselski, Jiří Rosický: Nearly locally presentable categories,
Theory and Appl. of Categories 33 (2018), #10, p.253-264;
http://www.tac.mta.ca/tac/volumes/33/10/33-10abs.html https://arxiv.org/abs/1710.10476
category-theory functors representable-functor hom-functor locally-presentable-categories
category-theory functors representable-functor hom-functor locally-presentable-categories
edited 3 hours ago
Martin Sleziak
44.3k7115266
asked 20 hours ago
user122424
1,0641616
edited 3 hours ago
Martin Sleziak
44.3k7115266
asked 20 hours ago
user122424
1,0641616
edited 3 hours ago
Martin Sleziak
44.3k7115266
edited 3 hours ago
Martin Sleziak
44.3k7115266
edited 3 hours ago
Martin Sleziak
44.3k7115266
44.3k7115266
asked 20 hours ago
user122424
1,0641616
asked 20 hours ago
user122424
1,0641616
asked 20 hours ago
user122424
1,0641616
1,0641616
To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago
add a comment |
To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago
To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago
add a comment |
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To preserve special directed colimits, which are by definition always coproducts, just with a richer diagram shape than the discrete one, you would have to preserve coproducts.
– Kevin Carlson
16 hours ago
I do not follow the meaning of the middle part of your sentence: " just with a richer diagram shape than the discrete one"
– user122424
14 hours ago
It's a coproduct expressed as a filtered colimit of sub-coproducts of up to size $lambda$ rather than as a discrete colimit. But it's still required to be a coproduct.
– Kevin Carlson
13 hours ago