Closure operators and their middle-interchange law |
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Authors: | Walter Tholen |
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Institution: | Dept. of Mathematics and Statistics, York University, Toronto, Canada |
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Abstract: | The paper presents a new definition of closure operator which encompasses the standard Dikranjan-Giuli notion, as well as the Bourn-Gran notion of normal closure operator. As is well known, any two closure operators C, D in a category may be composed in, within order, two different ways. For a subobject M→X one may consider DX(CXM) or DCX(M)(M) as the value at M of a new closure operator D⋅C or D?C, respectively. The two binary operations are linked by a lax middle-interchange law. This paper explores situations in which the law holds strictly. |
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Keywords: | 18A32 18A20 |
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