Pushout Invariance Revisited
-
Anthony W. Hager
and
Jorge Martínez
Abstract
With modest standing assumptions on a category C, it is shown that a Galois connection exists between subclasses of C-objects (on the one hand) and classes of epimorphisms of C (on the other). In this connection the following classes are in a one-to-one correspondence, which reverses inclusion: the epireflective classes of C-objects with the classes ε of epimorphisms which are pushout invariant, in the sense that, for each pushout diagram
in which e ∈ ε, then it follows that n ∈ ε. The paper then examines some of the consequences of this result, and in so doing “revisits” the pushout invariance of the authors as it was discussed in a paper of some fifteen years ago.
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© Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
Articles in the same Issue
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
