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LinearAlgebraForCAP

Category of Matrices over a Field for CAP

2025.08-02

25 August 2025

Sebastian Gutsche
Email: sebastian.gutsche@gmail.com
Homepage: https://sebasguts.github.io/
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Sebastian Posur
Email: sebastian.posur@uni-muenster.de
Homepage: https://sebastianpos.github.io
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Fabian Zickgraf
Email: f.zickgraf@dashdos.com
Homepage: https://github.com/zickgraf/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Category of Matrices

1.1 Constructors

  1.1-1 MatrixCategory
  1.1-2 VectorSpaceMorphism
  1.1-3 VectorSpaceObject
  1.1-4 MatrixCategoryObject
  1.1-5 MatrixCategory_as_CategoryOfRows

  1.2-1 UnderlyingFieldForHomalg
  1.2-2 UnderlyingMatrix
  1.2-3 UnderlyingFieldForHomalg
  1.2-4 Dimension

1.3 GAP Categories

1.3-1 IsVectorSpaceMorphism
1.3-2 IsVectorSpaceObject

2 Examples and Tests

2.1 Basic Commands

2.3 Solving (Homogeneous) Linear Systems

2.4 Homology object

2.6 Monoidal structure

2.7 MorphismFromSourceToPushout and MorphismFromFiberProductToSink

2.8 Opposite category

2.9 PreComposeList and PostComposeList

2.10 Split epi summand

2.12 FiberProduct

2.13 WrapperCategory

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