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Keywords:
inverse categories; inverse monoids; split idempotents; pointed sets; annihilators; exact sequences
inverse categories; inverse monoids; split idempotents; pointed sets; annihilators; exact sequences
Summary:
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.
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