Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Span composition using fake pullbacks   The construction of a category of spans can be made in some categories $\CC$
which do not have pullbacks in the traditional sense. The PROP for monoids is a
good example of such a $\CC$. 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.\v{S}. 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.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess