Algebraic theories in toposes

1978 ◽  
pp. 141-242 ◽  
Author(s):  
Peter T. Johnstone ◽  
Gavin C. Wraith
Keyword(s):  
Algebraic Theories

Elgot’s Analysis of Monadic Computation

1982 ◽  
Vol 5 (2) ◽  
pp. 171-186
Author(s):  
Stephen L. Bloom
Keyword(s):  
Algebraic Theories

A review is given of some of the late C.C. Elgot’s ideas on the syntax and semantics of monadic flowchart algorithms. In particular, the motivation for his “iterative algebraic theories” is explained.

Dagger extension theorem

2011 ◽  
Vol 21 (5) ◽  
pp. 1035-1066 ◽  
Author(s):  
Z. ÉSIK ◽  
T. HAJGATÓ
Keyword(s):  
Unique Solution ◽  
Extension Theorem ◽  
Sufficient Condition ◽  
Iteration Theory ◽  
Additive Structure ◽  
Algebraic Theories ◽  
Constant Morphism

Partial iterative theories are algebraic theories such that for certain morphisms f the equation ξ = f ⋅ 〈ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories.In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

Algebraic theories and algebraic categories

2011 ◽  
pp. 10-20
Author(s):  
J. Adamek ◽  
J. Rosicky ◽  
E. M. Vitale ◽  
F. W. Lawvere
Keyword(s):  
Algebraic Theories

XVIII.—The Invariant Theory of Forms in Six Variables relating to the Line Complex

1927 ◽  
Vol 46 ◽  
pp. 210-222 ◽  
Author(s):  
H. W. Turnbull
Keyword(s):  
Invariant Theory ◽  
Line Geometry ◽  
Five Dimensions ◽  
Ordinary Space ◽  
Homogeneous Coordinates ◽  
Plücker Coordinates ◽  
Algebraic Theories ◽  
Straight Line ◽  
Image Position ◽  
Theory Of Forms

It is well known that the Plücker coordinates of a straight line in ordinary space satisfy a quadratic identitywhich may also be considered as the equation of a point-quadric in five dimensions, if the six coordinates Pij are treated as six homogeneous coordinates of a point. Projective properties of line geometry may therefore be treated as projective properties of point geometry in five dimensions. This suggests that certain algebraic theories of quaternary forms (corresponding to the geometry of ordinary space) can best be treated as algebraic theories of senary forms: that is, forms in six homogeneous variables.

Algebraic Theories and Program Schemes

1982 ◽  
pp. 139-156
Author(s):  
Calvin C. Elgot
Keyword(s):  
Algebraic Theories
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