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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 Puppe-exact 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 EM-spans and that EM-spans admit fake pullbacks so that spans of EM-spans compose. Our setting is more general than Puppe-exact categories. We mention the formalism of distributive laws which, in a generalized form, would cover our setting.
Original language | English |
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Pages (from-to) | 102-117 |
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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Dive into the research topics of 'Span composition using fake pullbacks'. Together they form a unique fingerprint.Projects
- 2 Finished
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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
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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