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Martti Karvonen
Martti Karvonen
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An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then provingone proves a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then proving a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then one proves a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

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Martti Karvonen
Martti Karvonen
  • 631
  • 5
  • 10

An inverse category can be defined as a category where every $f$ admits ana unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then proving a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

An inverse category can be defined as a category where every $f$ admits an unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then proving a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

An inverse category can be defined as a category where every $f$ admits a unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then proving a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.

Source Link
Martti Karvonen
Martti Karvonen
  • 631
  • 5
  • 10

An inverse category can be defined as a category where every $f$ admits an unique regular inverse, i.e. a map $g$ such that $fgf=f$ and $gfg=g$. In [1], Kastl proves that any locally small inverse category admits a faithful functor into $PInj$, the category of sets and partial injections. The proof first verifies Isbell's criterion, obtaining a faithful functor to $Set$ and then proving a general result giving rise to a faithful functor to $PInj$.

[1] J. Kastl. Inverse categories. Studien zur Algebra und ihre Anwendungen, 7:51– 60, 1979.