inverse categories; inverse monoids; split idempotents; pointed sets; annihilators; exact sequences
We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.
 Kastl, J.: Inverse categories
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| Zbl 0427.18003
 Schwab, E.: Image and inverse image mappings in exact inverse categories
. Boll. U.M.I. 18–B (1981), 831–845. MR 0641740
| Zbl 0477.18002