Pushout invariance revisited

Rok, strany: 2015, 387 - 404

With modest standing assumptions on a category $\mathbf{C}$, it is shown that a Galois connection exists between subclasses of $\mathbf{C}$-objects (on the one hand) and classes of epimorphisms of $\mathbf{C}$ (on the other). In this connection the following classes are in a one-to-one correspondence, which reverses inclusion: the epireflective classes of $\mathbf{C}$-objects with the classes $\mathcal{E}$ of epimorphisms which are pushout invariant, in the sense that, for each pushout diagram

$$ \xymatrix{A\ar[d]_f\ar[r]^e & B\ar[d]^f' C\ar[r]_n & P} $$

in which $e\in\mathcal{E}$, then it follows that $n\in\mathcal{E}$. 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.

ISO 690:

Hager, A., Martínez, J. 2015. Pushout invariance revisited. In Mathematica Slovaca, vol. 65, no.2, pp. 387-404. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0030

APA:

Hager, A., Martínez, J. (2015). Pushout invariance revisited. Mathematica Slovaca, 65(2), 387-404. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0030