Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-simplicial Types in Logic-enriched Homotopy Type Theory   The problem of defining Semi-Simplicial Types (SSTs) in Homotopy Type Theory
(HoTT) has been recognized as important during the Year of Univalent
Foundations at the Institute of Advanced Study. According to the interpretation
of HoTT in Quillen model categories, SSTs are type-theoretic versions of Reedy
fibrant semi-simplicial objects in a model category and simplicial and
semi-simplicial objects play a crucial role in many constructions in homotopy
theory and higher category theory. Attempts to define SSTs in HoTT lead to some
difficulties such as the need of infinitary assumptions which are beyond HoTT
with only non-strict equality types.
  Voevodsky proposed a definition of SSTs in Homotopy Type System (HTS), an
extension of HoTT with non-fibrant types, including an extensional strict
equality type. However, HTS does not have the desirable computational
properties such as decidability of type checking and strong normalization. In
this paper, we study a logic-enriched homotopy type theory, an alternative
extension of HoTT with equational logic based on the idea of logic-enriched
type theories. In contrast to Voevodskys HTS, all types in our system are
fibrant and it can be implemented in existing proof assistants. We show how
SSTs can be defined in our system and outline an implementation in the proof
assistant Plastic.

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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat