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Abstract
The construction of a category of spans can be made in some categories A which do not have pullbacks in the traditional sense. The PROP for monoids is a good example of such an A . The 2012 book concerning homological algebra by Marco Grandis gives the proof of associativity of relations in a Puppeexact category based on a 1967 paper of M.’. Calenko. The proof here is a restructuring of that proof in the spirit of the first sentence of this Abstract. We observe that these relations are spans of EMspans and that EMspans admit fake pullbacks so that spans of EMspans compose. Our setting is more general than Puppeexact categories. We mention the formalism of distributive laws which, in a generalized form, would cover our setting.
Original language  English 

Pages (fromto)  102117 
Number of pages  16 
Journal  Theory and Applications of Categories 
Volume  36 
Issue number  4 
Publication status  Published  2021 
Keywords
 span
 partial map
 factorization system
 relation
 Puppe exact category
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Working synthetically in higher categorical structures
Lack, S., Verity, D., Garner, R. & Street, R.
19/06/19 → 18/06/22
Project: Other

Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research