| C. Lair, Etude G'en'erale de la Cat'egorie des esquisses, Esquisses Math. 24 (1974). |
....operation in will be interpreted as a subalgebra inclusion ( together with a homomorphism ( Furthermore, in order for these interpretations to yield a algebra structure in , the axioms must be satisfied. In a way analogous to algebraic theories [25, 17] to lim theories [40] and to sketches [23], there is then a theory in partial membership equational logic such that ( Notice that we could have chosen a bigger poset of subalgebra inclusions, yielding a looser definition of ( A natural choice for would have been the set of weak subalgebra inclusions. This would yield a notion of ....
C. Lair, Etude G'en'erale de la Cat'egorie des esquisses, Esquisses Math. 24 (1974).
.... A B constitute a poset category of canonical inclusions, it is possible to define the category PAlg T (PAlg T 0 ) for any two theories T = Omega ; Gamma) and T 0 = Omega 0 ; Gamma 0 ) Moreover, in a way analogous to algebraic theories [45, 29] to lim theories [31] and to sketches [42], in [58] the construction of a tensor theory T Omega T 0 in partial membership equational logic is given such that PAlg T Omega T 0 PAlg T (PAlg T 0 ) PAlg T 0 (PAlg T ) Notice that we could have chosen a bigger poset of subalgebra inclusions, yielding a looser definition of PAlg T ....
C. Lair. Etude G'en'erale de la Cat'egorie des esquisses. Esquisses Math. 24. 1974.
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