Composing PROPs.
A note on the exact completion of a regular category, and its infinitary generalizations.
Bicat is not triequivalent to Gray.
The 3-by-3 lemma for regular Goursat categories.
On the monadicity of categories with chosen colimits.
The extensive completion of a distributive category.
-Cat is locally presentable or locally bounded if is so.
On property-like structures.
Coalgebras, braidings, and distributive laws.
Adhesive and quasiadhesive categories
We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Adhesive and quasiadhesive categories
We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
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