* further references on semi-categories
@ 2005-11-29 9:14 Thomas Streicher
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From: Thomas Streicher @ 2005-11-29 9:14 UTC (permalink / raw)
To: categories
In order to provide a categorical semantics of typed $\lambda$-calculus
without $\eta$-rule Susumu Hayashi used semicategories in
MR0841025 (87i:18005) Hayashi, Susumu
Adjunction of semifunctors: categorical structures
in nonextensional lambda calculus.
Theoret. Comput. Sci. 41 (1985), no. 1, 95--104.
This was later taken up by R.Hoofman in his Thesis on "Nonstable Models
of Linear Logic" (see the first 7 items when you type in "Hoofman, R*"
in Math.Reviews).
However, in my opinion for the purpose of modelling $\lambda\beta$-calculus
it is more natural to use the following kind of structures: (small) categories
\C with finite products such that y(Y)^{y(X)} (taken in Psh(\C)) is a retract
of some y(E).
Thomas Streicher
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2005-11-29 9:14 further references on semi-categories Thomas Streicher
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