Category theory using 2-sorted logic
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Can anyone give some reference text that axiomatizes category theory using first order logic using 2 sorts (if that makes sense)? I have found reference about 1 sorted axiomatization but I also found that 1 sorted and 2 sorted axiomatizations are not exactly the same. I am studying set theory built from category theory (ETCS) so I would like axiomatizations be built not in ZFC metatheory, but in some weak theory like PRA.
I would also appreciate any comments about it, for example, how perspective and useful set theory built from category theory is.
reference-request category-theory foundations
asked Nov 14 at 21:07
Daniels Krimans
43228
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Can anyone give some reference text that axiomatizes category theory using first order logic using 2 sorts (if that makes sense)? I have found reference about 1 sorted axiomatization but I also found that 1 sorted and 2 sorted axiomatizations are not exactly the same. I am studying set theory built from category theory (ETCS) so I would like axiomatizations be built not in ZFC metatheory, but in some weak theory like PRA.
I would also appreciate any comments about it, for example, how perspective and useful set theory built from category theory is.
reference-request category-theory foundations
asked Nov 14 at 21:07
Daniels Krimans
43228
1
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Can anyone give some reference text that axiomatizes category theory using first order logic using 2 sorts (if that makes sense)? I have found reference about 1 sorted axiomatization but I also found that 1 sorted and 2 sorted axiomatizations are not exactly the same. I am studying set theory built from category theory (ETCS) so I would like axiomatizations be built not in ZFC metatheory, but in some weak theory like PRA.
I would also appreciate any comments about it, for example, how perspective and useful set theory built from category theory is.
reference-request category-theory foundations
asked Nov 14 at 21:07
Daniels Krimans
43228
Can anyone give some reference text that axiomatizes category theory using first order logic using 2 sorts (if that makes sense)? I have found reference about 1 sorted axiomatization but I also found that 1 sorted and 2 sorted axiomatizations are not exactly the same. I am studying set theory built from category theory (ETCS) so I would like axiomatizations be built not in ZFC metatheory, but in some weak theory like PRA.
I would also appreciate any comments about it, for example, how perspective and useful set theory built from category theory is.
reference-request category-theory foundations
reference-request category-theory foundations
asked Nov 14 at 21:07
Daniels Krimans
43228
asked Nov 14 at 21:07
Daniels Krimans
43228
asked Nov 14 at 21:07
Daniels Krimans
43228
asked Nov 14 at 21:07
Daniels Krimans
43228
asked Nov 14 at 21:07
Daniels Krimans
43228
43228
1
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42
add a comment |
1
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42
1
1
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42
add a comment |
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1
This really comes across as three questions: a reference request for a particular axiomatization of categories; a request for an axiomatization in PRA, whatever this means here; and a vague question about the merits of ETCS. These are each better suited as separate questions.
– Malice Vidrine
Nov 15 at 0:07
@MaliceVidrine Do you feel that if I just said that " I am looking for reference text that axiomatizes category theory using first order logic using 2 sorts " would be better?
– Daniels Krimans
Nov 15 at 2:42