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Crossed modules of monoids II. Relative crossed modules. (arXiv:1803.04124v1 [math.CT])
来源于:arXiv
This is the second part of a series of three strongly related papers in which
three equivalent structures are studied:
- internal categories in categories of monoids; defined in terms of pullbacks
relative to a chosen class of spans
- crossed modules of monoids relative to this class of spans
- simplicial monoids of so-called Moore length 1 relative to this class of
spans.
The most important examples of monoids that are covered are small categories
(treated as monoids in categories of spans) and bimonoids in symmetric monoidal
categories (regarded as monoids in categories of comonoids). In this second
part we define relative crossed modules of monoids and prove their equivalence
with the relative categories of Part I. 查看全文>>