GDCT User Guide: Category Tools
Contents
1. Product Selecting Tools Product opens a dialogue window allowing selection of a possible product object from the current category from a drop down and specification of possibly composite first and second projections then testing the span for being a product Page 16 of 36 WARNING The domain of each projection must be the possible product object The test is only valid on a confluent category If in doubt use the Make Confluent tool NOTE This feature has not yet been implemented Page 17 of 362. SECTION 4 CATEGORY TOOLS Make Confluent Select Tools Make Confluent This command applies the Knuth Bendix algorithm to the currently displayed category with arrows ordered in their storage order Mo relations added to category The set of reductions is now confluent El cancel Relations which are added to the current category are reported To add these relations to the current category click Ok or click Cancel to keep the category in its current from Equality of Composites To test two possibly composite arrows for equality in the current category select Tools Equality of Composites A dialogue allows entry of two paths f GDCT E quality of Composites Category Name cube Results 2 1 and 3 0 are NOT equal First Fath 2 1 Second Fath 3 0 H Equality OK WARNING The category must be confluent for valid results Domains and codomains of paths must match Make Dual Category This tool will create the opposite category of the currently displayed category Select Tools Make Dual A dialogue window opens prompting for the name of the dual After the user provides the name the dual category is displayed WARNING The opposite category is NOT SAVED automatically when it is created use File Save Page 15 of 36 Category if you wish to save the dual Initial Object Select Tools Initial Object This command tests objects of the current category chosen by a dial
3. ogue for initiality For each selected object which is not initial a reason is given fe GDCT Check Category for Initial Object s Current Category A MOT INITIAL cube 11 5 0 and 7 3 0 are both paths to object H Select Object s to Check B NOT INITIAL 11 5 and 7 3 are both paths to abject H T MOT INITIAL 10 6 and 2 are both paths to abject H D MOT INITIAL ho path to abject A I amp 7 bees Ei Select All Check Object s OK WARNING This command will not operate correctly unless the category has a confluent set of relations If in doubt use Make Confluent tool first Sum Selecting Tools Sum opens a dialogue window allowing selection of a possible sum object from the current category from a drop down and specification of possibly composite first and second injections then testing the cospan for being a sum WARNING The codomain of each injection must be the possible sum object The test is only valid on a confluent category If in doubt use the Make Confluent tool NOTE This feature has not yet been implemented Terminal Object Select Tools Terminal Object This command tests objects of the current category chosen by a dialogue for being terminal For each selected object which is not terminal a reason is given WARNING This command will not operate correctly unless the category has a confluent set of relations If in doubt use Make Confluent Tool first
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