Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unified Functorial Signal Representation III: Foundations, Redundancy,
  $L^0$ and $L^2$ functors   In this paper we propose and lay the foundations of a functorial framework
for representing signals. By incorporating additional category-theoretic
relative and generative perspective alongside the classic set-theoretic measure
theory the fundamental concepts of redundancy, compression are formulated in a
novel authentic arrow-theoretic way. The existing classic framework
representing a signal as a vector of appropriate linear space is shown as a
special case of the proposed framework.
  Next in the context of signal-spaces as a categories we study the various
covariant and contravariant forms of $L^0$ and $L^2$ functors using categories
of measurable or measure spaces and their opposites involving Boolean and
measure algebras along with partial extension. Finally we contribute a novel
definition of intra-signal redundancy using general concept of isomorphism
arrow in a category covering the translation case and others as special cases.
Through category-theory we provide a simple yet precise explanation for the
well-known heuristic of lossless differential encoding standards yielding
better compressions in image types such as line drawings, iconic image, text
etc; as compared to classic representation techniques such as JPEG which choose
bases or frames in a global Hilbert space.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
37
The categories of this paper are: supr-con