nForum - Search Results Feed (Tag: finite)2020-07-11T19:49:17-04:00https://nforum.ncatlab.org/
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twosets_nonames20170618https://nforum.ncatlab.org/discussion/7854/2017-06-18T14:12:47-04:002017-06-18T14:12:47-04:00Peter Heinighttps://nforum.ncatlab.org/account/1588/
created [[twosets_nonames20170618]]
created [[twosets_nonames20170618]]
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twosets_op_with_names20170618https://nforum.ncatlab.org/discussion/7853/2017-06-18T14:11:19-04:002017-06-18T14:11:19-04:00Peter Heinighttps://nforum.ncatlab.org/account/1588/
created [[twosets_op_with_names20170618]], which is Illustration of opposite of the category that [[twosets20170617]] is an illustration of.[[twosets_op_with_names20170618]] is identical to ...
created [[twosets_op_with_names20170618]], which is Illustration of opposite of the category that [[twosets20170617]] is an illustration of.

[[twosets_op_with_names20170618]] is identical to [[twosets_op_nonames20170618]] except for the morphisms having names.
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twosets_op_nonames20170618https://nforum.ncatlab.org/discussion/7852/2017-06-18T14:08:36-04:002017-06-18T14:08:36-04:00Peter Heinighttps://nforum.ncatlab.org/account/1588/
created [[twosets_op_nonames20170618]]
created [[twosets_op_nonames20170618]]
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objects of finite type (terminology)https://nforum.ncatlab.org/discussion/7701/2017-04-21T04:48:35-04:002017-04-25T05:20:45-04:00Alain BruguiÃ¨reshttps://nforum.ncatlab.org/account/1579/
Hi, If x is an object of a category C, one usually says that x is if finite presentation (or compact) if for any direct filtered system (y_i) in C, the canonical mapf : colim_i Hom(x,y_i) -> ...
Hi, If x is an object of a category C, one usually says that x is if finite presentation (or compact) if for any direct filtered system (y_i) in C, the canonical map

f : colim_i Hom(x,y_i) -> Hom(x, colim y_i)

is bijective. One usually says x is of finite type if this holds only for direct filtered systems of monomophisms.

However, I am interested in objects x for which f is injective (without additional condition on the direct filtered system). It seems to me that, in the category of (right) modules over a ring, such objects are exactly finitely generated modules. My question is, has this been considered, and is there a name for this property of x?