Lawvere's 1989 preprint on "Intrinsic boundary"

Lawvere's 1989 preprint on "Intrinsic boundary"

[Ryszard Paweł Kostecki]

Dear all,

I am searching for Bill Lawvere's 1989 preprint "Intrinsic boundary in
certain mathematical toposes exemplify ‘logical’ operators not passively
preserved by substitution". It is not available in the internet, nor at
any library indexed by worldcat.org. Is there a chance that someone
reading this email has a copy of it?

(I have a copy of his 1991 text "Intrinsic co-Heyting boundaries and the
Leibniz rule in certain toposes", and I am searching specifically for
this 1989 preprint.)

With best wishes
Ryszard




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adequate and coadequate subcategories

[Posina Venkata Rayudu]

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Dear All,

For some time, I have been staring at the basic relation of algebraic
geometry (https://zenodo.org/records/7079058<https://url.au.m.mimecastprotect.com/s/wvP_CP7L1NfLvjO6u6TO9V?domain=zenodo.org>, p. 2), which is an
adjoint relation between geometry and algebra:

V^Yop <===> (V^Y)op

which Professor F. William Lawvere was kind enough to suggest as a
framework to abstract the mathematical content of the fundamental
dialectic of philosophy:

([epistemology vs. ontology] vs. reality)

I think compounding epistemology and ontology into which reality is
resolved is a major outstanding scientific program. Surely, Newton
would be happy, having emphasized synthesis after analysis.

Professor F. William Lawvere referred to the above adjointness as
Isbell conjugacy
(http://www.tac.mta.ca/tac/reprints/articles/8/tr8.pdf<https://url.au.m.mimecastprotect.com/s/zq5yCQnM1WfwB28RSAZ2f-?domain=tac.mta.ca>, p. 17). Simply
put, Isbell conjugacy is about getting to know a category V in terms
of geometric Y-shaped figures vs. algebraic Y-valued properties
(https://zenodo.org/records/7059109<https://url.au.m.mimecastprotect.com/s/zK-HCRONg6s3nMJOSQX2Fw?domain=zenodo.org>, p. 49).

Going by our experience with sets, a single-element set 1 = {*} is
adequate enough to completely characterize every set and to test for
the equality of functions, but we need a two-element coadequate set 2
= {false, true} to tell apart elements of any domain set.

Before long I can't help but wonder if the relationship between

V^Aop <=?=> (V^C)op

(where A and C are adequate and coadequate subcategories,
respectively, of a category V) would be relatively more informative
than the above Isbell conjugacy.

Furthermore, in a CatList post (06 March 2009), Professor F. William
Lawvere points out that Isbell conjugacy is a special case of the
construction of the total category with two descriptions which
objectify adjointness (unfortunately I couldn't find any mention of
'total category' in a quick search of his Functorial Semantics of
Algebraic Theories
(http://www.tac.mta.ca/tac/reprints/articles/5/tr5.pdf<https://url.au.m.mimecastprotect.com/s/j5ybCVARmOHp0W7ZuESkx2?domain=tac.mta.ca>, which he
cites).

I look forward to your corrections and suggestions!

Happy Bakrid :)

Thanking you,
Yours truly,
posina


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